Updated on 2023/02/06

YAMANAKA, Yoshiya

Scopus Paper Info
Paper Count: 0  Citation Count: 0  h-index: 5

Citation count denotes the number of citations in papers published for a particular year.

Affiliation
Faculty of Science and Engineering, School of Fundamental Science and Engineering
Job title
Professor
Homepage URL

Concurrent Post

• Faculty of Science and Engineering   Graduate School of Fundamental Science and Engineering

Research Institute

• 2022
-
2024

Waseda Research Institute for Science and Engineering   Concurrent Researcher

Degree

• 早稲田大学   博士(理学)

• Waseda University (Japan)   Doctor of Science

Professional Memberships

•

Japan Physical Society of Japan

Research Areas

• Theoretical studies related to particle-, nuclear-, cosmic ray and astro-physics

• Mathematical physics and fundamental theory of condensed matter physics

Research Interests

• Elementary Particles Physics,Nuclear Physics & Cosmic Ray Physics

Papers

• Semiclassical Analysis of Driven-Dissipative Excitonic Condensation

R. Imai, J. Takahashi, T. Oyama, Y. Yamanaka

PROCEEDINGS OF THE 14TH ASIA-PACIFIC PHYSICS CONFERENCE   2319  2021

View Summary

A theoretical study of excitonic condensation in a driven-dissipative semiconductor is presented. The system that we analyze is driven by a coherent light that creates electron-hole pairs and also includes the process of the annihilation of the pairs. To study the steady state realized in this nonequilibrium system. we employ the Schwinger-Keldysh path integral formalism, which is useful for discussing the semiclassical aspect. We derive an effective theory for the excitonic condensation in the driven-dissipative situation and present a condition on the amplitude and phase of the condensate.

• Quantum fluctuations of zero-modes for trapped two-component Bose-Einstein condensates

Junichi Takahashi, Yuto Hayaki, Yoshiya Yamanaka

PROCEEDINGS OF THE 14TH ASIA-PACIFIC PHYSICS CONFERENCE   2319  2021

View Summary

Zero-mode operators associated with a spontaneous breakdown of internal symmetry are often suppressed and their quantum fluctuations are neglected owing to the absence of a definite criterion for determining the ground state and infrared divergences in physical quantities. Because the zero-mode fluctuations for systems with finite-size and spatially inhomogeneity cannot be neglected, we have proposed a novel treatment of the zero-mode for finite systems, which helps determine the unique ground state and evaluate the physical quantities without divergence. Following the proposed treatment, we consider trapped systems with two-component Bose-Einstein condensates. The results obtained demonstrate that the interaction strength between the two components considerably affect the dynamical properties, illustrating the importance of the zero-mode for finite systems.

• J Takahashi, Y Yamanaka, S Ohkubo

Progress of Theoretical and Experimental Physics   2020 ( 9 ) 093D03/1 - 12  2020.09  [Refereed]  [International journal]

1
Citation
(Scopus)
• Supersolidity of the α cluster structure in the nucleus 12C

S. Ohkubo, J. Takahashi, Y. Yamanaka

Progress of Theoretical and Experimental Physics   2020 ( 4 ) 1 - 11  2020.04  [Refereed]

• Dynamical properties of the finite-size Dicke model coupled to a thermal reservoir

R. Imai, Y. Yamanaka

J. Phys. Soc. Jpn.   88   024401-1 - 024401-7  2019.01  [Refereed]

2
Citation
(Scopus)
• J. Takahashi, R. Katsuragi, Y. Kazama, Y. Nakamura, Y. Yamanaka, S. Ohkubo

AIP Conference Proceedings   2038   020024  2018.11  [Refereed]

• Stability of symmetry breaking states in finite-size Dicke model with photon leakage

R. Imai, Y. Yamanaka

Phys. Lett. A   382   3333 - 3338  2018.11  [Refereed]

1
Citation
(Scopus)
• Bose--Einstein condensation of alpha clusters and new soft mode in 12C-52Fe 4N nuclei in field theoretical superfluid cluster model

R. Katsuragi, Y. Kazama, J. Takahashi, Y. Nakamura, Y. Yamanaka, S. Ohkubo

Phys. Rev. C   98   044303 (18pages)  2018.10  [Refereed]

8
Citation
(Scopus)
• Self-energy renormalization for inhomogeneous nonequilibrium systems and field expansion via complete set of time-dependent wavefunctions

Y. Kuwahara, Y. Nakamura, Y. Yamanaka

International Journal of Modern Physics B   32 ( 10 ) 1850111 (22 pages)  2018.04  [Refereed]

View Summary

The way to determine the renormalized energy of inhomogeneous systems of a quantum field under an external potential is established for both equilibrium and nonequilibrium scenarios based on thermo field dynamics. The key step is to find an extension of the on-shell concept valid in homogeneous case. In the nonequilibrium case, we expand the field operator by time-dependent wavefunctions that are solutions of the appropriately chosen differential equation, synchronizing with temporal change of thermal situation, and the quantum transport equation is derived from the renormalization procedure. Through numerical calculations of a triple-well model with a reservoir, we show that the number distribution and the time-dependent wavefunctions are relaxed consistently to the correct equilibrium forms at the long-term limit.

1
Citation
(Scopus)
• Thermal and quantum fluctuations of confined Bose-Einstein condensate beyond the Bogoliubov approximation

Y. Nakamura, T. Kawaguchi, Y. Torii, Y. Yamanaka

ANNALS OF PHYSICS   376   484 - 498  2017.01  [Refereed]

View Summary

The formulation for zero mode of a Bose-Einstein condensate beyond the Bogoliubov approximation at zero temperature [Y. Nakamura et al., Phys. Rev. A 89 (2014) 013613] is extended to finite temperature. Both thermal and quantum fluctuations are considered in a manner consistent with a concept of spontaneous symmetry breakdown for a finite-size system. Therefore, we need a proper treatment of the zero mode operators, which invoke non-trivial enhancements in depletion condensate and thermodynamical quantities such as the specific heat. The enhancements are visible in the weak interaction case. Our approach reproduces the results of a homogeneous system in the Bogoliubov approximation in a large particle number limit. (C) 2016 Elsevier Inc. All rights reserved.

5
Citation
(Scopus)
• Effective field theory of Bose-Einstein condensation of a clusters and Nambu-Goldstone-Higgs states in C-12

Y. Nakamura, J. Takahashi, Y. Yamanaka, S. Ohkubo

PHYSICAL REVIEW C   94 ( 1 ) 014314  2016.07  [Refereed]

View Summary

An effective field theory of alpha-cluster condensation is formulated as a spontaneously broken symmetry in quantum field theory to understand the raison d'etre and the nature of the Hoyle and alpha-cluster states in C-12. The Nambu-Goldstone and Higgs mode operators in infinite systems are replaced with a pair of canonical operators whose Hamiltonian gives rise to discrete energy states in addition to the Bogoliubov-de Gennes excited states. The calculations reproduce well the experimental spectrum of the alpha-cluster states. The existence of the Nambu-Goldstone-Higgs states is demonstrated and crucial. The gamma-decay transitions are also obtained.

14
Citation
(Scopus)
• Effective field theory of Bose-Einstein condensation of α clusters and Nambu-Goldstone-Higgs states in C 12

Nakamura, Y, Nakamura, Y, Takahashi, J, Takahashi, J, Yamanaka, Y, Ohkubo, S, Ohkubo, S

Physical Review C - Nuclear Physics   94 ( 1 ) 014314 (8 pages)  2016.07  [Refereed]

View Summary

© 2016 American Physical Society.An effective field theory of α-cluster condensation is formulated as a spontaneously broken symmetry in quantum field theory to understand the raison d'être and the nature of the Hoyle and α-cluster states in C12. The Nambu-Goldstone and Higgs mode operators in infinite systems are replaced with a pair of canonical operators whose Hamiltonian gives rise to discrete energy states in addition to the Bogoliubov-de Gennes excited states. The calculations reproduce well the experimental spectrum of the α-cluster states. The existence of the Nambu-Goldstone-Higgs states is demonstrated and crucial. The γ-decay transitions are also obtained.

14
Citation
(Scopus)
• Analytical study of parameter regions of dynamical instability for two-component Bose-Einstein condensates with coaxial quantized vortices

M. Hoashi, Y. Nakamura, Y. Yamanaka

PHYSICAL REVIEW A   93 ( 4 )  2016.04  [Refereed]

View Summary

The dynamical instability of weakly interacting two-component Bose-Einstein condensates with coaxial quantized vortices is analytically investigated in a two-dimensional isotopic harmonic potential. We examine whether complex eigenvalues appear on the Bogoliubov-de Gennes equation, implying dynamical instability. Rather than solving the Bogoliubov-de Gennes equation numerically, we rely on a perturbative expansion with respect to the coupling constant which enables a simple, analytic approach. For each pair of winding numbers and for each magnetic quantum number, the ranges of intercomponent coupling constant where the system is dynamically unstable are exhaustively obtained. Corotating and counter-rotating systems show distinctive behaviors. The latter is much more complicated than the former with respect to dynamical instability, particularly because radial excitations contribute to complex eigenvalues in counter-rotating systems.

3
Citation
(Scopus)
• Analytical study of parameter regions of dynamical instability for two-component Bose-Einstein condensates with coaxial quantized vortices

Hoashi, M, Hoashi, M, Nakamura, Y, Yamanaka, Y

Physical Review A - Atomic, Molecular, and Optical Physics   93 ( 4 ) 043622 (9 pages)  2016.04  [Refereed]

View Summary

© 2016 American Physical Society.The dynamical instability of weakly interacting two-component Bose-Einstein condensates with coaxial quantized vortices is analytically investigated in a two-dimensional isotopic harmonic potential. We examine whether complex eigenvalues appear on the Bogoliubov-de Gennes equation, implying dynamical instability. Rather than solving the Bogoliubov-de Gennes equation numerically, we rely on a perturbative expansion with respect to the coupling constant which enables a simple, analytic approach. For each pair of winding numbers and for each magnetic quantum number, the ranges of intercomponent coupling constant where the system is dynamically unstable are exhaustively obtained. Corotating and counter-rotating systems show distinctive behaviors. The latter is much more complicated than the former with respect to dynamical instability, particularly because radial excitations contribute to complex eigenvalues in counter-rotating systems.

3
Citation
(Scopus)
• 19aAC-10 Analysis of Quantum Field Theory on Nα-cluster based on Picture of Bose-Einstein Condensation

Yamanaka Y., Nakamura Y., Nagai Y., Yosioka R., Ohkubo S.

Meeting Abstracts of the Physical Society of Japan   71   178 - 178  2016

• Interacting multiple zero mode formulation and its application to a system consisting of a dark soliton in a condensate

J. Takahashi, Y. Nakamura, Y. Yamanaka

PHYSICAL REVIEW A   92 ( 2 ) 023627 (6 pages)  2015.08  [Refereed]

View Summary

To formulate the zero modes in a finite-size system with spontaneous breakdown of symmetries in quantum field theory is not trivial, for in the naive Bogoliubov theory, one encounters difficulties such as phase diffusion, the absence of a definite criterion for determining the ground state, and infrared divergences. An interacting zero mode formulation that has been proposed for systems with a single zero mode to avoid these difficulties is extended to general systems with multiple zero modes. It naturally and definitely gives the interactions among the quantized zero modes, the consequences of which can be observed experimentally. In this paper, as a typical example, we consider an atomic Bose-Einstein condensed system with a dark soliton that contains two zero modes corresponding to the spontaneous breakdown of the U(1) gauge and translational symmetries. Then we evaluate the standard deviations of the zero mode operators and see how the mutual interaction between the two zero modes affects them.

3
Citation
(Scopus)
• 17pPSA-31 Zero mode quantum fluctuation for Bose-Einstein condensate of cold atomic gas with attractive interaction

Nakamura Y., Kawaguchi T., Yamanaka Y.

Meeting Abstracts of the Physical Society of Japan   70   2684 - 2684  2015

• 22pPSB-11 Zero modes and their quantum state for gray soliton in cold atomic gas

Nakamura Y., Kawaguchi T., Takahashi J., Yamanaka Y.

Meeting Abstracts of the Physical Society of Japan   70   3047 - 3047  2015

• 22pPSB-13 Quantum state of soliton and its depletion

Takahashi J., Nakamura Y., Yamanaka Y.

Meeting Abstracts of the Physical Society of Japan   70   3049 - 3049  2015

• Dynamical instability induced by the zero mode under symmetry breaking external perturbation

J. Takahashi, Y. Nakamura, Y. Yamanaka

ANNALS OF PHYSICS   347   250 - 260  2014.08  [Refereed]

View Summary

A complex eigenvalue in the Bogoliubov-de Gennes equations for a stationary Bose-Einstein condensate in the ultracold atomic system indicates the dynamical instability of the system. We also have the modes with zero eigenvalues for the condensate, called the zero modes, which originate from the spontaneous breakdown of symmetries. Although the zero modes are suppressed in many theoretical analyses, we take account of them in this paper and argue that a zero mode can change into one with a pure imaginary eigenvalue by applying a symmetry breaking external perturbation potential. This emergence of a pure imaginary mode adds a new type of scenario of dynamical instability to that characterized by the complex eigenvalue of the usual excitation modes. For illustration, we deal with two one-dimensional homogeneous Bose-Einstein condensate systems with a single dark soliton under a respective perturbation potential, breaking the invariance under translation, to derive pure imaginary modes. (C) 2014 Elsevier Inc. All rights reserved.

3
Citation
(Scopus)
• Numerical Analysis of Quantum Transport Equation for Bose Gas in One Dimensional Optical Lattice

Y. Kuwahara, Y. Nakamura, Y. Yamanaka

JPS Conf. Proc.   1   012101 (5 pages)  2014.03  [Refereed]

• Relationship between Dynamical Instability and Zero Modes for Dark Soliton in Bose-Einstein Condensate

J. Takahashi, Y. Nakamura, Y. Yamanaka

JPS Conf. Proc.   1   012100 (4 pages)  2014.03  [Refereed]

• Analysis of Particle Transfer for Periodic Lattice Modulation in Three Dimensional Optical Lattice

M. Inoue, Y. Nakamura, Y. Yamanaka

JPS Conf. Proc.   1   012099 (4 pages)  2014.03  [Refereed]

• Nonequilibrium Thermo Field Dynamics for Thermal Relaxation Process of Confined Cold Atomic Gas

Y. Nakamura, Y. Kuwahara, Y. Yamanaka

JPS Conf. Proc.   1   012098 (5 pages)  2014.03  [Refereed]

• Analysis of Particle Transfer by Periodic Lattice Modulation for Ultracold Fermionic Atom Systems in Three-Dimensional Optical Lattice

Motoyoshi Inoue, Yusuke Nakamura, Yoshiya Yamanaka

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   83 ( 2 ) 024604 (6 pages)  2014.02  [Refereed]

View Summary

We analyze an ultracold fermionic atom system in a three-dimensional optical lattice with a confinement harmonic potential, using the Hubbard model and a time-dependent Gutzwiller variational approach to numerical calculation. Our study is focused on the time evolution of particle transfer when the lattice potential is modulated by adding a periodic one. The choice of parameters, such as the modulation frequency, modulation amplitude, and number of particles, affects particle transfer. We calculate the time evolution of the variance in the particle distribution and show its dependences on the parameters. Lattice modulation is found to effectively control particle transfer, and is a useful method in experiments on fermionic atom systems.

• Analysis of Particle Transfer by Periodic Lattice Modulation for Ultracold Fermionic Atom Systems in Three-Dimensional Optical Lattice

Motoyoshi Inoue, Yusuke Nakamura, Yoshiya Yamanaka

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   83 ( 2 ) 024604 (6 pages)  2014.02  [Refereed]

View Summary

We analyze an ultracold fermionic atom system in a three-dimensional optical lattice with a confinement harmonic potential, using the Hubbard model and a time-dependent Gutzwiller variational approach to numerical calculation. Our study is focused on the time evolution of particle transfer when the lattice potential is modulated by adding a periodic one. The choice of parameters, such as the modulation frequency, modulation amplitude, and number of particles, affects particle transfer. We calculate the time evolution of the variance in the particle distribution and show its dependences on the parameters. Lattice modulation is found to effectively control particle transfer, and is a useful method in experiments on fermionic atom systems.

• Formulation for the zero mode of a Bose-Einstein condensate beyond the Bogoliubov approximation

Y. Nakamura, J. Takahashi, Y. Yamanaka

Physical Review A - Atomic, Molecular, and Optical Physics   89 ( 1 ) 013613 (5 pages)  2014.01  [Refereed]

View Summary

The unperturbed Hamiltonian for the Bose-Einstein condensate, which includes not only the first and second powers of the zero mode operators but also the higher ones, is proposed to determine a unique and stationary vacuum at zero temperature. From the standpoint of quantum field theory, it is done in a consistent manner that the canonical commutation relation of the field operator is kept. In this formulation, the condensate phase does not diffuse and is robust against the quantum fluctuation of the zero mode. The standard deviation for the phase operator depends on the condensed atom number with the exponent of -1/3, which is universal for both homogeneous and inhomogeneous systems. © 2014 American Physical Society.

14
Citation
(Scopus)
• From classical mechanics with doubled degrees of freedom to quantum field theory for nonconservative systems

Y. Kuwahara, Y. Nakamura, Y. Yamanaka

PHYSICS LETTERS A   377 ( 43 ) 3102 - 3105  2013.12  [Refereed]

View Summary

The 2 x 2-matrix structure of Green's functions is a common feature for the real-time formalisms of quantum field theory under thermal situations, such as the closed time path formalism and Thermo Field Dynamics (TFD). It has been believed to originate from quantum nature. Recently, Galley has proposed the Hamilton's principle with initial data for nonconservative classical systems, doubling each degree of freedom [1]. We show that the Galley's Hamilton formalism can be extended to quantum field and that the resulting theory is naturally identical with nonequilibrium TFD. (C) 2013 Elsevier B.V. All rights reserved.

6
Citation
(Scopus)
• From superoperator formalism to nonequilibrium Thermo Field Dynamics

Y. Nakamura, Y. Yamanaka

Annals of Physics   331   51 - 69  2013.04  [Refereed]

View Summary

Emphasizing that the specification of the representation space or the quasiparticle picture is essential in nonequilibrium quantum field system, we have constructed the unique unperturbed representation of the interaction picture in the superoperator formalism. To achieve it, we put the three basic requirements (the existence of the quasiparticle picture at each instant of time, the macroscopic causality and the relaxation to equilibrium). From the resultant representation follows the formulation of nonequilibrium Thermo Field Dynamics (TFD). The two parameters, the number distribution and excitation energy, characterizing the representation, are to be determined by the renormalization condition. While we point out that the diagonalization condition by Chu and Umezawa is inconsistent with the equilibrium theory, we propose a new renormalization condition as a generalization of the on-shell renormalization on the self-energy which derives the quantum transport equation and determines the renormalized excitation energy. © 2012 Elsevier Inc.

7
Citation
(Scopus)
• 水谷 友一, 稲垣 知宏, 中村 祐介, 山中 由也

素粒子論研究   119 ( 4 ) F51 - F53  2012

• Canonical Quantization for a Relativistic Neutral Scalar Field in Non-Equilibrium Thermo Field Dynamics

Yuichi Mizutani, Tomohiro Inagaki, Yusuke Nakamura, Yoshiya Yamanaka

PROGRESS OF THEORETICAL PHYSICS   126 ( 4 ) 681 - 701  2011.10  [Refereed]

View Summary

A relativistic neutral scalar held is investigated in non-equilibrium thermo field dynamics. The canonical quantization is applied to the fields out of equilibrium. Because the thermal Bogoliubov transformation becomes time-dependent, the equations of motion for the ordinary unperturbed creation and annihilation operators are modified. This forces us to introduce a thermal counter term in the interaction Hamiltonian which generates additional radiative corrections. Imposing the self-consistency renormalization condition on the total radiative corrections, we obtain the quantum Boltzmann equation for the relativistic scalar field.

6
Citation
(Scopus)
• Effects of finite temperature on the robustness of the Mott insulator phase in pseudo two dimensional Bose-Hubbard model

M. Inoue, K. Kobayashi, Y. Nakamura, Y. Yamanaka

J. Phys. B: At. Mol. Opt. Phys.   44 ( 16 ) 165303(9pp)  2011.08  [Refereed]

1
Citation
(Scopus)
• Effects of finite temperature on the robustness of the Mott insulator phase in a pseudo-two-dimensional Bose-Hubbard model

Motoyoshi Inoue, Keita Kobayashi, Yusuke Nakamura, Yoshiya Yamanaka

JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS   44 ( 16 ) 165303 (9pp)  2011.08  [Refereed]

View Summary

We study the superfluid-Mott insulator (SF-MI) transition in a two-dimensional optical lattice system and employ the Bose-Hubbard model in three dimensions with a combined potential of an optical lattice in two directions and a confining harmonic trap in the other direction, which we refer to as the pseudo-two-dimensional Bose-Hubbard model. Some excited states with respect to the harmonic trap are taken into account in this paper. The Mott lobes shrink in the mu and J directions of the mu-J phase diagram. The shrinkage occurs because the interactions involving the excited states become weaker than that between particles in the ground state. The dispersion of the in-site particle number increases because the energy spacing between the eigenstates of the Hamiltonian decreases at finite temperature. The presence of the excited states significantly affects the robustness of the MI phase at finite temperature.

1
Citation
(Scopus)
• Extension of Nelson&apos;s stochastic quantization to finite temperature using thermo field dynamics

K. Kobayashi, Y. Yamanaka

PHYSICS LETTERS A   375 ( 37 ) 3243 - 3249  2011.08  [Refereed]

View Summary

We present an extension of Nelson&apos;s stochastic quantum mechanics to finite temperature. Utilizing the formulation of Thermo Field Dynamics (TFD), we can show that Ito&apos;s stochastic equations for tilde and non-tilde particle positions reproduce the TFD-type Schrodinger equation which is equivalent to the Liouville-von Neumann equation. In our formalism, the drift terms in the Ito&apos;s stochastic equation have the temperature dependence and the thermal fluctuation is induced through the correlation of the non-tilde and tilde particles. We show that our formalism satisfies the position-momentum uncertainty relation at finite temperature. (C) 2011 Elsevier B.V. All rights reserved.

2
Citation
(Scopus)
• Unifying treatment of nonequilibrium and unstable dynamics of cold bosonic atom system with time-dependent order parameter in Thermo Field Dynamics

Y. Nakamura, Y. Yamanaka

ANNALS OF PHYSICS   326 ( 4 ) 1070 - 1083  2011.04  [Refereed]

View Summary

The coupled equations which describe the temporal evolution of the Bose-Einstein condensed system are derived in the framework of nonequilibrium Thermo Field Dynamics. The key element is that they are not the naive assemblages of assumed equations, but are the self-consistent ones derived by appropriate renormalization conditions. While the order parameter is time-dependent, an explicit quasiparticle picture is constructed by a time-dependent expansion. Our formulation is valid even for the system with a unstable condensate, and describes the condensate decay caused by the Landau instability as well as by the dynamical one. (C) 2010 Elsevier Inc. All rights reserved.

6
Citation
(Scopus)
• Soryushiron Kenkyu Electronics   118 ( 4 ) D147 - D149  2011

• Soryushiron Kenkyu Electronics   118 ( 4 ) D153 - D155  2011

• Derivation of non-Markovian transport equations for trapped cold atoms in nonequilibrium thermal field theory

Y. Nakamura, T. Sunaga, M. Mine, M. Okumura, Y. Yamanaka

ANNALS OF PHYSICS   325 ( 2 ) 426 - 441  2010.02  [Refereed]

View Summary

The non-Markovian transport equations for the systems of cold Bose atoms confined by a external potential both without and with a Bose-Einstein condensate are derived in the framework of non-equilibrium thermal field theory (Thermo Field Dynamics). Our key elements are an explicit particle representation and a self-consistent renormalization condition which are essential in thermal field theory. The non-Markovian transport equation for the non-condensed system, derived at the two-loop level, is reduced in the Markovian limit to the ordinary quantum Boltzmann equation derived in the other methods. For the condensed system, we derive a new transport equation with an additional collision term which becomes important in the Landau instability. (C) 2009 Elsevier Inc. All rights reserved.

6
Citation
(Scopus)
• Analytical study of the splitting process of a multiply-quantized vortex in a Bose-Einstein condensate and collaboration of the zero and complex modes

K. Kobayashi, Y. Nakamura, M. Mine, Y. Yamanaka

ANNALS OF PHYSICS   324 ( 11 ) 2359 - 2371  2009.11  [Refereed]

View Summary

We study the dynamics of a trapped Bose-Einstein condensate with a multiply-quantized vortex, and investigate the roles of the fluctuations in the dynamical evolution of the system. Using the perturbation theory of the external potential, and assuming the situation of the small coupling constant of self-interaction, we analytically solve the time-dependent Gross-Pitaevskii equation. We introduce the zero mode and its adjoint mode of the Bogoliubov-de Gennes equations. Those modes are known to be essential for the completeness condition. We confirm how the complex eigenvalues induce the vortex splitting. It is shown that the physical role of the adjoint zero mode is to ensure the conservation of the total condensate number. The contribution of the adjoint mode is exponentially enhanced in synchronism with the exponential growth of the complex mode, and is essential in the vortex splitting. (C) 2009 Elsevier Inc. All rights reserved.

3
Citation
(Scopus)
• Nonequilibrium TFD for systems of trapped cold atoms

Y. Yamanaka, M. Okumura, M. Mine, Y. Nakamura

素粒子論研究   116   F75 - F77  2009.02

• Quantum field theoretical analysis on unstable behavior of Bose-Einstein condensates in optical lattices

K. Kobayashi, M. Mine, M. Okumura, Y. Yamanaka

ANNALS OF PHYSICS   323 ( 5 ) 1247 - 1270  2008.05  [Refereed]

View Summary

We study the dynamics of Bose-Einstein condensates flowing in optical lattices on the basis of quantum field theory. For such a system, a Bose-Einstein condensate shows an unstable behavior which is called the dynamical instability. The unstable system is characterized by the appearance of modes with complex eigenvalues. Expanding the field operator in terms of excitation modes including complex ones, we attempt to diagonalize the unperturbative Hamiltonian and to find its eigenstates. It turns out that although the unperturbed Hamiltonian is not diagonalizable in the conventional bosonic representation the appropriate choice of physical states leads to a consistent formulation. Then we analyze the dynamics of the system in the regime of the linear response theory. Its numerical results are consistent with those given by the discrete nonlinear Schrodinger equation. (c) 2007 Elsevier Inc. All rights reserved.

• Condition for emergence of complex eigenvalues in the Bogoliubov-de Gennes equations

Y. Nakamura, M. Mine, M. Okumura, Y. Yamanaka

PHYSICAL REVIEW A   77 ( 4 ) 043601  2008.04  [Refereed]

View Summary

The condition for the appearance of dynamical instability of the Bose-condensed system, characterized by the emergence of complex eigenvalues in the Bogoliubov-de Gennes equations, is studied analytically. It is concluded that the degeneracy between a positive-norm eigenmode and a negative-norm one is essential for the emergence of complex modes. Based on the conclusion, we justify the two-mode approximation applied in our previous work [E. Fukuyama , Phys. Rev. A 76, 043608 (2007)], in which we analytically studied the condition for the existence of complex modes when the condensate has a highly quantized vortex.

18
Citation
(Scopus)
• Soryushiron Kenkyu Electronics   116 ( 2 ) B110 - B112  2008

• Soryushiron Kenkyu Electronics   116 ( 2 ) B64 - B66  2008

• 中村 祐介, 峰 真如, 奥村 雅彦, 山中 由也

素粒子論研究   116 ( 2 ) B67 - B69  2008

• Condition for the existence of complex modes in a trapped Bose-Einstein condensate with a highly quantized vortex

E. Fukuyama, M. Mine, M. Okumura, T. Sunaga, Y. Yamanaka

PHYSICAL REVIEW A   76 ( 4 )  2007.10  [Refereed]

View Summary

We consider a trapped Bose-Einstein condensate (BEC) with a highly quantized vortex. For the BEC with a doubly, triply, or quadruply quantized vortex, the numerical calculations have shown that the Bogoliubov-de Gennes equations, which describe the fluctuation of the condensate, have complex eigenvalues. In this paper, we obtain the analytic expression of the condition for the existence of complex modes, using the method developed by Rossignoli and Kowalski [R. Rossignoli and A. M. Kowalski, Phys. Rev. A 72, 032101 (2005)] for the small coupling constant. To derive it, we make the two-mode approximation. With the derived analytic formula, we can identify the quantum numbers of the complex modes for each winding number of the vortex. Our result is consistent with those obtained by the numerical calculation in the case that the winding number is two, three, or four. We prove that the complex modes always exist when the condensate has a highly quantized vortex.

5
Citation
(Scopus)
• Quantum field theoretical description of unstable behavior of trapped Bose-Einstein condensates with complex eigenvalues of Bogoliubov-de Gennes equations

Makoto Mine, Masahiko Okumura, Tomoka Sunaga, Yoshiya Yamanaka

ANNALS OF PHYSICS   322 ( 10 ) 2327 - 2349  2007.10  [Refereed]

View Summary

7 The Bogoliubov-de Gennes equations are used for a number of theoretical works on the trapped Bose-Einstein condensates. These equations are known to give the energies of the quasi-particles when all the eigenvalues are real. We consider the case in which these equations have complex eigenvalues. We give the complete set including those modes whose eigenvalues are complex. The quantum fields which represent neutral atoms are expanded in terms of the complete set. It is shown that the state space is an indefinite metric one and that the free Hamiltonian is not diagonalizable in the conventional bosonic representation. We introduce a criterion to select quantum states describing the metastablity of the condensate, called the physical state conditions. In order to study the instability, we formulate the linear response of the density against the time-dependent external perturbation within the regime of Kubo's linear. response theory. Some states, satisfying all the physical state conditions, give the blow-up and damping behavior of the density distributions corresponding to the complex eigenmodes. It is qualitatively consistent with the result of the recent analyses using the time-dependent Gross-Pitaevskii equation. (c) 2007 Elsevier Inc. All rights reserved.

14
Citation
(Scopus)
• Condition for the existence of complex modes in a trapped Bose-Einstein condensate with a highly quantized vortex (vol 76, art no 043608, 2007)

E. Fukuyama, M. Mine, M. Okumura, T. Sunaga, Y. Yamanaka

PHYSICAL REVIEW A   76 ( 4 ) 43608  2007.10  [Refereed]

• The condition for existence of complex modes in trapped Bose-Einstein condensate with a highly quantized vortex

Tomoka Sunaga, Eriko Fukuyama, Makoto Mine, Masahiko Okumura, Yoshiya Yamanaka

JOURNAL OF LOW TEMPERATURE PHYSICS   148 ( 3-4 ) 381 - 386  2007.08  [Refereed]

View Summary

We consider a trapped Bose-Einstein condensate with a highly quantized vortex. Pu et al. found numerically the parameter region in which complex eigenvalues arise. Recently, the splitting of a highly quantized vortex into two singly quantized vortices is observed in the experiment. We derive analytically the condition for the existence of complex eigenvalues by using the small coupling constant expansion and the two-mode approximation. We check that our results agree with those by Pu et al.

2
Citation
(Scopus)
• Quantum field theoretical description of dynamical instability of trapped Bose-Einstein condensates

Makoto Mine, Masahiko Okumura, Tomoka Sunaga, Yoshiya Yamanaka

JOURNAL OF LOW TEMPERATURE PHYSICS   148 ( 3-4 ) 331 - 336  2007.08  [Refereed]

View Summary

The Bogoliubov-de Gennes equations are used for a number of theoretical works on the trapped Bose-Einstein condensates. We consider the case in which these equations have complex eigenvalues. We give the complete set including a pair of complex modes whose eigenvalues are complex conjugate to each other. The expansion of the quantum fields which represent neutral atoms in terms of the complete set brings about the operators associated with the complex modes, which are simply neither bosonic nor fermionic ones. The eigenstate of the Hamiltonian is given. Introducing the notion of the physical states, we discuss the instability of the condensates in the context of Kubo's linear response theory.

3
Citation
(Scopus)
• Quantum field theoretical description of unstable behavior of a Bose-Einstein condensate with a highly quantized vortex in a harmonic potential

M. Okumura, M. Mine, T. Sunaga, Y. Yamanaka

LASER PHYSICS   17 ( 2 ) 211 - 214  2007.02  [Refereed]

View Summary

The Bogoliubov-de Gennes equations are used for a number of theoretical works to describe quantum and thermal fluctuations of trapped Bose-Einstein condensates. We consider the case in which the condensate has a highly quantized vortex. It is known that these equations have complex eigenvalues in this case. We give the complete set including a pair of complex modes whose eigenvalues are complex conjugates to each other. The expansion of the quantum fields which represent neutral atoms in terms of the complete set brings the operators associated with the complex modes, which are simply neither bosonic nor fermionic ones. The eigenstate of the Hamiltonian is given. Introducing the notion of the physical states, we discuss the instability of the condensates in the context of Kubo's linear response theory.

• Complex Eigenvalues Associated with Trapped BEC and Field Theoretical Description of Unstable Behavior

M. Mine, M. Okumura, Y. Yamanaka

素粒子論研究   114   C24 - C26  2006.12

• Goldstone theorem, Hugenholtz-Pines theorem, and Ward-Takahashi relation in finite volume Bose-Einstein condensed gases

Hiroaki Enomoto, Masahiko Okumura, Yoshiya Yamanaka

ANNALS OF PHYSICS   321 ( 8 ) 1892 - 1917  2006.08  [Refereed]

View Summary

We construct an approximate scheme based on the concept of the spontaneous symmetry breakdown, satisfying the Goldstone theorem, for finite volume Bose-Einstein condensed gases in both zero and finite temperature cases. In this paper, we discuss the Bose-Einstein condensation in a box with periodic boundary condition and do not assume the thermodynamic limit. When energy spectrum is discrete, we found that it is necessary to deal with the Nambu-Goldstone mode explicitly without the Bogoliubov's prescription, in which zero-mode creation- and annihilation-operators are replaced with a c-number by hand, for satisfying the Goldstone theorem. Furthermore, we confirm that the unitarily inequivalence of vacua in the spontaneous symmetry breakdown is true for the finite volume system. (c) 2006 Elsevier Inc. All rights reserved.

8
Citation
(Scopus)
• Unitarily inequivalent vacua in Bose-Einstein condensation of trapped gases

Masahiko Okumura, Yoshiya Yamanaka

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS   365 ( 2 ) 429 - 445  2006.06  [Refereed]

View Summary

We approach the problem of the Bose-Einstein condensation of neutral atoms in an external trap, which is a finite system in size, from the viewpoint of quantum field theory. The phenomenon is considered as a spontaneous symmetry breakdown. The main result of this paper is that the vacua for this system with finite size and finite number of trapped neutral atoms, parametrized by different phases of the order parameter, are orthogonal to each other, namely the Fock spaces associated with each vacuum are unitarily inequivalent to each other. In the proof, the zero-energy mode which is the Nambu-Goldstone mode, and is discrete due to the presence of the trap, plays a crucial role. We introduce the discrete zero-energy mode in the formulation of the generalized Bogoliubov transformation and introduce an additional infinitesimal symmetry-breaking term in the Hamiltonian to control the zero-energy mode properly. (c) 2005 Elsevier B.V. All rights reserved.

2
Citation
(Scopus)
• Effect of the zero-mode on the response of a trapped bose-condensed gas

M Mine, T Koide, M Okumura, Y Yamanaka

PROGRESS OF THEORETICAL PHYSICS   115 ( 4 ) 683 - 700  2006.04  [Refereed]

View Summary

The dynamical response of a trapped Bose-Einstein condensate (BEC) is formulated consistently with quantum field theory and is numerically evaluated. We regard the BEC as a manifestation of the breaking of the global phase symmetry. Then, the Goldstone theorem implies the existence of a zero energy excitation mode (the zero-mode). We calculate the effect of the zero-mode on the response frequency and show that the contribution of the zero-mode to the first excitation mode is not so important in the parameter set realized in the existing experiment. This is the reason that experimental results can be described using the Bogoliubov prescription, although it breaks the consistency of the description in quantum field theory.

2
Citation
(Scopus)
• Soryushiron Kenkyu Electronics   114 ( 3 ) C27 - C29  2006

• Effect of zero mode on the response of napped bose-condensed atoms

M. Mine, T. Koide, M. Okumura, Y. Yamanaka

THIRD 21COE SYMPOSIUM: ASTROPHYSICS AS INTERDISCIPLINARY SCIENCE   31   211 - +  2006  [Refereed]

View Summary

The response of the trapped Bose-Einstein condensate (BEC) is investigated. We regard the BEC as a manifestation of the spontaneous breakdown of the global phase symmetry. Then, the Goldstone theorem leads to the existence of the zero energy excitation mode (zero-mode). We calculate the effect of the zero-mode to the response frequency and show that the contribution of the zero-mode to the first excitation mode becomes dominant as the temperature and/or the coupling constant are increased.

• Approximate scheme satisfying the Goldstone theorem in finite volume Bose-Einstein condensed gas

H. Enomoto, M. Okumura, Y. Yamanaka

素粒子論研究   112   C55 - C57  2005.12

• Bose-Einstein condensation and macroscopic wave function in quantum field theory

M. Okumura, M. Mine, Y. Yamanaka

素粒子論研究   112   C45 - C54  2005.12

• Relation between generalized Bogoliubov and Bogoliubov-de Gennes approaches including Nambu-Goldstone mode

M Mine, M Okumura, Y Yamanaka

JOURNAL OF MATHEMATICAL PHYSICS   46 ( 4 ) 42307  2005.04  [Refereed]

View Summary

The two approaches of consistent quantum field theory for systems of the trapped Bose-Einstein condensates are known, one is the Bogoliubov-de Gennes approach and the other is the generalized Bogoliubov approach. In this paper, we investigate the relation between the two approaches and show that they are formally equivalent to each other. To do this one must carefully treat the Nambu-Goldstone mode which plays a crucial role in the condensation. It is emphasized that the choice of vacuum is physically relevant. (C) 2005 American Institute of Physics.

9
Citation
(Scopus)
• Ward-Takahashi relation at finite temperature in Bose-Einstein condensation of trapped neutral atoms

M Okumura, Y Yamanaka

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS   348   157 - 172  2005.03  [Refereed]

View Summary

We prove that the Ward-Takahashi relations at finite temperature are satisfied at the tree level for a system of a trapped Bose-Einstein condensate when the zero mode is included in the quasi-particle picture property. This implies that the zero mode represents the Nambu-Goldstone mode and that it is introduced in a way consistent with the Goldstone theorem. In the proof, we employ thermo field dynamics which is a real-time operator formalism of quantum field theory at finite temperature. (C) 2004 Published by Elsevier B.V.

5
Citation
(Scopus)
• M. Okumura, Y. Yamanaka

素粒子論研究   110 ( 5 ) E16 - E18  2005.02

• M. Okumura, Y. Yamanaka

素粒子論研究   108 ( 5 ) E43 - E45  2004.02

• Effects of quantum coordinates on condensate density in a trapped Bose-Einstein condensate

M Okumura, Y Yamanaka

PROGRESS OF THEORETICAL PHYSICS   111 ( 2 ) 199 - 211  2004.02  [Refereed]

View Summary

The effects of quantum coordinates associated with the Nambu-Goldstone mode in a trapped Bose-Einstein condensate are investigated at zero and finite temperatures. We develop a loop expansion and perform numerical calculations over a wide range of temperature, i.e., between zero and the critical temperatures. Our results are compared with those obtained in cases without the Nambu-Goldstone mode (the Bogoliubov approximation) and with the Nambu-Goldstone mode as a zero-energy particle mode.

6
Citation
(Scopus)
• Soryushiron Kenkyu Electronics   108 ( 5 ) E40 - E42  2004

• Response of trapped Bose-Einstein condensates under time-dependent perturbation

T. Koide, M. Mine, M. Okumura, Y. Yamanaka

Journal of Modern Optics   51-6 ( 7 ) 1103 - 1104  2004  [Refereed]

1
Citation
(Scopus)
• Nambu-Goldstone mode in trapped bose-einstein condensation

M. Okumura, Y. Yamanaka

Journal of Modern Optics   51-6 ( 7 ) 1101 - 1102  2004  [Refereed]

• Role of Nambu-Goldstone Mode in Trapped Bose-Einstein Condensation

Y. Yamanaka, M. Okumura, M. Mine

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN   72   152 - 155  2003.11  [Refereed]

View Summary

The system of the trapped Bose-Einstein condensation is investigated from the viewpoint of Quantum Field Theory. It is pointed out that the Nambu-Goldstone mode, which is a discrete mode due to the trapping potential, creates observable effects through fluctuations. The way how the Nambu-Goldstone mode is treated is not unique. The introduction of quantum coordinates is a possible candidate.

• Proper treatment of the zero mode in quantum field theory for trapped Bose-Einstein condensation

M Okumura, Y Yamanaka

PHYSICAL REVIEW A   68 ( 1 ) 13609 - 13620  2003.07  [Refereed]

View Summary

So far much theoretical consideration of experiments on the Bose-Einstein condensation (BEC) of alkali-metal atoms in harmonic traps is based on the Gross-Pitaevskii (GP) equation. In this paper, we attempt to formulate the BEC in the language of quantum field theory and to estimate the quantum and thermal fluctuation effects, which are neglected in the approximation using the GP equation. First, the formulation at zero temperature is developed, and then it is extended to the finite-temperature case by means of thermofield dynamics. We treat the zero-energy mode with care, so that the canonical commutation relations hold. As a result, an infrared divergence appears, but it can be renormalized into the observed condensate number. Numerical calculations are performed. For illustration, the corrections at one-loop level to the original GP equation are given. We also calculate numerically the effects of quantum and thermal fluctuations on the distribution of condensed atoms.

• The Role of Nambu-Goldstone Mode in Trapped Bose-Einstein Condensates

M. Okumura, Y. Yamanaka

素粒子論研究/京都大学   106   E12 - E12  2003.02

• Proper treatment of the zero mode in quantum field theory for trapped Bose-Einstein condensation

M. Okumura, Y. Yamanaka

Physical Review A - Atomic, Molecular, and Optical Physics   68 ( 1 ) 12  2003  [Refereed]

View Summary

So far much theoretical consideration of experiments on the Bose-Einstein condensation (BEC) of alkali-metal atoms in harmonic traps is based on the Gross-Pitaevskii (GP) equation. In this paper, we attempt to formulate the BEC in the language of quantum field theory and to estimate the quantum and thermal fluctuation effects, which are neglected in the approximation using the GP equation. First, the formulation at zero temperature is developed, and then it is extended to the finite-temperature case by means of thermofield dynamics. We treat the zero-energy mode with care, so that the canonical commutation relations hold. As a result, an infrared divergence appears, but it can be renormalized into the observed condensate number. Numerical calculations are performed. For illustration, the corrections at one-loop level to the original GP equation are given. We also calculate numerically the effects of quantum and thermal fluctuations on the distribution of condensed atoms. © 2003 The American Physical Society.

• M. Okumura, Y. Yamanaka

素粒子論研究   105 ( 1 ) A89 - A91  2002.04

View Summary

We analyze the Nambu-Goldstone (NG) mode for a system of trapped Bose-Einstein condensation (BEC). The NG mode is a discrete mode in our case, contrary to the homogeneous case in which the NG mode is in a continuum labeled by a momentum index. In order to control the NG mode, an infinitesimal symmetry-breaking term is introduced. This breaking term plays the role of infinitesimal magnetic field in spin system which fixes the macroscopic "direction" of spin. We calculate a tadpole diagram to evaluate fluctuation effects, taking account of the NG mode, then find that the coefficient of the wave function of condensation is infrared divergent while the remaining terms are finite.

• Nonequilibrium TFD (Thrmo Field Dynamics)-Review

Y. Yamanaka

素粒子論研究   105   A73 - A82  2002.04

• 奥村 雅彦, 山中 由也

素粒子論研究   105 ( 3 ) C15 - C17  2002

• M. Okumura, Y. Yamanaka

素粒子論研究   103 ( 1 ) A35 - A38  2001.04

View Summary

The Bose-Einstein condensation in recent experiments is formulated as a problem in thermal quantum field theory. From this formulation, we carry out numerical analysis so as to investigate effects of quantum and thermal fluctuation to the condensate phase and properties of quasi-particles in this situation.

• Quantum Correction to the Gross-Pitaevskii Equation in a Bose--Einstein Condensate

M. Okumura, Y. Yamanaka

物性研究   75   1039 - 1049  2001.02

• M. Okumura, Y. Yamanaka

素粒子論研究   100 ( 5 ) E110 - E113  2000.02

View Summary

Experiments of Bose-Einstein condensation (BEC) of alkali atoms in harmonic traps which were achieved successfully have inspired various theoretical studies. So far many theoretical considerations are based on the Gross-Pitaevskii equation. In this report, we attempt to formulate the BEC in the language of quantum field theory, so that effects of quantum fluctuation can be estimated properly.

• Fluctuation of the Bose-Einstein condensate in a trap

H. Ezawa, K. Nakamura, K. Watanabe, Y. Yamanaka

Mathematical Physics and Stochastic Analysis-Essays in Honour of Ludwig Streit/ World Scientific     169 - 183  2000.01  [Refereed]

• Tunneling time based on the quantum diffusion process approach in multi-channel and optical potential cases

Ohba, I, K Imafuku, Y Yamanaka

PRAMANA-JOURNAL OF PHYSICS   51 ( 5 ) 603 - 614  1998.11  [Refereed]

View Summary

We analyze the effects of inelastic scattering on the tunneling time theoretically, using generalized Nelson's quantum mechanics. This generalization enables us to describe quantum system with channel couplings and optical potential in a real time stochastic approach, which seems to give us a new insight into quantum mechanics beyond Copenhagen interpretation.

• Imafuku Kentaro, Ohba Ichiro, Yamanaka Yoshiya

京都大学数理解析研究所講究録   982   30 - 40  1997.03

• Effects of inelastic scattering on tunneling time based on the generalized diffusion process approach

Kentaro Imafuku, Ichiro Ohba, Yoshiya Yamanaka

Physical Review A - Atomic, Molecular, and Optical Physics   56 ( 2 ) 1142 - 1153  1997  [Refereed]

View Summary

We analyze the effects of inelastic scattering on the tunneling time theoretically, using generalized Nelson’s quantum mechanics. This generalization enables us to describe a quantum system with optical potential and channel couplings in a real-time stochastic approach, which seems to give us a new insight into quantum mechanics beyond Copenhagen interpretation. © 1997 The American Physical Society.

22
Citation
(Scopus)
• Concept of quasiparticle in thermofield dynamics for nonequilibrium systems

Y Yamanaka, K Nakamura

PHYSICS ESSAYS   9 ( 4 ) 617 - 623  1996.12  [Refereed]

View Summary

The concept of quasiparticle (representation particle) is a central issue when thermofield dynamics (TFD) for nonequilibrium systems of quantum fields is constructed. The development of nonequilibrium TFD, mainly clone by the Alberta group, is reviewed from the viewpoint of the quasiparticle.

• Quantum dephasing by chaos

H Nakazato, M Namiki, S Pascazio, Y Yamanaka

PHYSICS LETTERS A   222 ( 3 ) 130 - 136  1996.10  [Refereed]

View Summary

We examine whether the chaotic behavior of classical systems with a limited number of degrees of freedom can produce quantum dephasing, against the conventional idea that dephasing takes place only in large systems with a huge number of constituents and complicated internal interactions. On the basis of this analysis, we briefly discuss the possibility of defining quantum chaos and of inventing a ''chaos detector''.

• Diffusion in inhomogeneous TFD

Y. Yamanaka, K. Nakamura

Thermal Field Theories and Their Applications/World Scientific     71 - 83  1996.06  [Refereed]

• Quasi particle modes in spatially inhomogeneous thermo field dynamics

K.Nakamura, Y. Yamanaka

Thermal Field Theories and Their Applications/World Scientific     23 - 31  1996.06  [Refereed]

• Thermal field theory in non-equilibrium states

PA Henning, K Nakamura, Y Yamanaka

INTERNATIONAL JOURNAL OF MODERN PHYSICS B   10 ( 13-14 ) 1599 - 1614  1996.06  [Refereed]

View Summary

Conventional transport theory is not really applicable to nonequilibrium systems which exhibit strong quantum effects. We present two different approaches to overcome this problem. Firstly we point out how transport equations may be derived that incorporate a nontrivial spectral function as a typical quantum effect, and test this approach in a toy model of a strongly interacting degenerate plasma. Secondly we explore a path to include nonequilibrium effects into quantum field theory through momentum mixing transformations in Fock space. Although the two approaches are completely orthogonal, they lead to the same coherent conclusion.

• Estimation of tunneling time based on the quantum diffusion process approach and netron scattering

I. Ohba, K. Imafuku, Y. Yamanaka

J. Phys. Soc. Jpn. Suppl. A   65   41 - 44  1996  [Refereed]

• Development of nonequilibrium TFD

Y. Yamanaka

Field Theory and Collective Phenomena/World Scientific     237 - 249  1995.12  [Refereed]

• TUNNELING TIME-BASED ON THE QUANTUM DIFFUSION PROCESS APPROACH

K IMAFUKU, OHBA, I, Y YAMANAKA

PHYSICS LETTERS A   204 ( 5-6 ) 329 - 335  1995.08  [Refereed]

View Summary

We present a time-dependent description of tunneling phenomena, using Nelson's stochastic approach. It appears to be capable to describe individual experimental runs, and provides a new insight into quantum measurement processes. We propose a new way to evaluate the tunneling time in this approach and give the results of numerical simulations.

• ENTROPY LAW FROM INHOMOGENEOUS THERMOFIELD DYNAMICS

Y YAMANAKA, K NAKAMURA

MODERN PHYSICS LETTERS A   9 ( 31 ) 2879 - 2891  1994.10  [Refereed]

View Summary

In the framework of thermofield dynamics for spatially inhomogeneous time-dependent nonequilibrium situations, we derive the kinetic equation, which is different from the Boltzmann equation due to quantum effects. It is shown that this kinetic equation leads to the entropy law. An expression for the entropy how is found.

• M. Namiki, Y. Yamanaka, S. Muroya

物性研究   62 ( 1 ) 171 - 181  1994.04

• THERMO-FIELD DYNAMICS IN TIME REPRESENTATION

Y YAMANAKA, H UMEZAWA, K NAKAMURA, T ARIMITSU

INTERNATIONAL JOURNAL OF MODERN PHYSICS A   9 ( 7 ) 1153 - 1180  1994.03  [Refereed]

View Summary

Making use of the thermo field dynamics (TFD) we formulate a calculable method for time-dependent nonequilibrium systems in a time representation (t-representation) rather than in the k0-Fourier representation. The corrected one-body propagator in the t-representation has the form of B-1 (diagonal matrix) B (B being a thermal Bogoliubov matrix). The number parameter in B here is the observed number (the Heisenberg number) with a fluctuation. With the usual definition of the on-shell self-energy a self-consistent renormalization condition leads to a kinetic equation for the number parameter. This equation turns out to be the Boltzmann equation, from which the entropy law follows.

• A TIME-DEPENDENT NONEQUILIBRIUM CALCULATIONAL SCHEME TOWARDS THE STUDY OF TEMPERATURE-FLUCTUATIONS

TS EVANS, HARDMAN, I, H UMEZAWA, Y YAMANAKA

FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS   41 ( 2 ) 151 - 175  1993  [Refereed]

View Summary

A new perturbative scheme for interacting nonequilibrium thermal quantum fields using thermo field dynamics is outlined by explicitly considering the temporal change of the thermal vacuum as it moves through many inequivalent state vector spaces. One is then naturally led to two sources of time dependence, one from the dynamics and the other from the change of thermal vacuum, which are taken care of by the Hamiltonian and the thermal generator, respectively. To obtain a practical scheme we restrict ourselves by the demand that a spectral representation for the full propagator exists. This leads to a time dependent temperature. The addition of a diagonalization condition for the quasi-particle Hamiltonian provides the master equation for the number density. We show that our formalism is equivalent to an extended form of the path-ordering method. This formalism is a first step towards the study of the origin of heat and temperature in high-energy heavy ion collisions.

• NONEQUILIBRIUM THERMOFIELD DYNAMICS - IN TIME REPRESENTATION

Y YAMANAKA

VISTAS IN ASTRONOMY, VOL 37, PTS 1-4   37   93 - 97  1993  [Refereed]

• QUANTUM-FIELD THEORY WITH FICTITIOUS TIME IN STOCHASTIC QUANTIZATION

Y YAMANAKA

PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT   111 ( 111 ) 417 - 431  1993  [Refereed]

View Summary

A model with spontaneous breakdown of symmetry in quantum field theory is studied in the framework of the Parisi-Wu stochastic quantization (SQ). Looking at the conventional treatment of the model in the canonical and the path-integral quantizations including the problems of many inequivalent Hilbert spaces and measures, we explicitly construct the SQ formulation for the model in the conventional treatment of quantum field theory. The real power of SQ is found in extending quantum field theory beyond the existing frameworks; SQ easily avoids the problems imposed by choices of Hilbert space or measure. We demonstrate it by introducing c-numbers depending on the fictitious time into the starting formal Langevin equations for the model. This new formulation in SQ thus obtained is mathematically well-defined, leading to a definite calculational scheme. The result from this shows that the masses and number of excitation modes change from those in the conventional treatment.

• TEMPORAL DESCRIPTION OF THERMAL QUANTUM-FIELDS

H UMEZAWA, Y YAMANAKA

MODERN PHYSICS LETTERS A   7 ( 37 ) 3509 - 3520  1992.12  [Refereed]

View Summary

By making use of time-dependent Bogoliubov transformations, we develop a calculation technique for time-dependent non-equilibrium systems of quantum fields in a time-representation (t-representation). The corrected one-body propagator in the t-representation turns out to have the form B-1 (diagonal matrix) B (B being a thermal Bogoliubov matrix). Applying the usual on-shell concept to the diagonal matrix part of the self-energy, we formulate a self-consistent renormalization scheme. This renormalization determines the vacuum and leads to a kinetic equation for the number density parameter, which reduces to the Boltzmann equation in the lowest approximation. This gives us the increasing entropy in time (the second law of thermodynamics).

• TIME-SPACE DEPENDENT FORMULATION IN THERMOFIELD DYNAMICS

K NAKAMURA, H UMEZAWA, Y YAMANAKA

MODERN PHYSICS LETTERS A   7 ( 38 ) 3583 - 3592  1992.12  [Refereed]

View Summary

The recently developed formulation of time-dependent non-equilibrium thermofield dynamics (TFD) is extended to spatially inhomogeneous field systems in this paper. This inhomogeneous formalism is constructed from introducing momentum mixing thermal Bogoliubov transformation. The momentum mixing number density in the Bogoliubov matrix is related to the number density distribution defined at each space-time point which is to be observed.

• Time-dependent TFD

Y. Yamanaka

物性研究   59   197 - 202  1992.11

• HEISENBERG AND INTERACTION REPRESENTATIONS IN THERMO FIELD-DYNAMICS

TS EVANS, HARDMAN, I, H UMEZAWA, Y YAMANAKA

JOURNAL OF MATHEMATICAL PHYSICS   33 ( 1 ) 370 - 378  1992.01  [Refereed]

View Summary

In this paper the so-called a degree of freedom appearing in thermal quantum field theory is discussed, using thermo field dynamics (TFD). This paper is confined to stationary thermal situations, both nonequilibrium and equilibrium. The main result is that when the stationary number distribution differs from the equilibrium one the use of time ordered and antitime ordered formalisms picks up alpha = 1 and alpha = 0, in contrast to the general belief that the Feynman diagram method is usable for any other alpha as well. This situation in TFD will be compared with the other approaches. The reason why the Feynman diagram method becomes available for any alpha in the case of the equilibrium distributions is also studied.

25
Citation
(Scopus)
• ON CLASSICAL PROPERTIES OF THERMAL SQUEEZED STATES

A MANN, M REVZEN, H UMEZAWA, Y YAMANAKA

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL   24 ( 19 ) 4527 - 4533  1991.10  [Refereed]

View Summary

We use the formalism of thermo field dynamics and the classical Cramer's theorem to show that if two quantum systems are prepared independently and their centre of mass is found to be a thermal squeezed state, then both systems were prepared in thermal squeezed states. This constitutes an alternative derivation of the quantum version of Cramer's theorem. Further, we consider the case of two systems that are prepared independently and their centre of mass is in a pure state in the expanded space of thermo field dynamics. In this case we show that the system is also separable in the centre of mass and relative coordinates, and again all the states involved are thermal squeezed states.

• THERMAL DEGREE OF FREEDOM IN THERMO FIELD-DYNAMICS

H UMEZAWA, Y YAMANAKA

PHYSICS LETTERS A   155 ( 2-3 ) 75 - 82  1991.05  [Refereed]

View Summary

The view of the thermal degree of freedom for the quantum field system, using the language of thermo field dynamics, is elaborated in this paper: the thermal degree of freedom is the degree of freedom to move through degenerate thermal vacua associated with spontaneous breakdown of a certain symmetry (G triple-over-dot-symmetry). Based on this view, we study a quasi-particle picture, in which the G triple-over-dot-transformation becomes the thermal Bogoliubov transformation.

• NOISE AND PARTICLE CONDENSATION

H UMEZAWA, Y YAMANAKA

PHYSICA A   170 ( 2 ) 291 - 305  1991.01  [Refereed]

View Summary

This paper is aimed to clarify the appearance of non-quantum noises in quantum systems in various subjects from a unified viewpoint. Examples taken are the squeezed state in quantum optics, the Hawking radiation around the black hole and thermo field dynamics (TFD) in thermal quantum field theory. Under the use of mathematical formulation of TFD, the origin of noises is traced to the Bogoliubov transformation, i.e., the pair condensation of bare particles in the physical vacua. Detailed analysis of the noise energy reveals a crucial distinction among them: Calling the operator generating the noise energy the noise generator, we find two cases, dynamical and spontaneous, depending on whether the noise generator is part of the Hamiltonian or not. The squeezed state belongs to the former, TFD does to the latter.

• SYMMETRIES IN STOCHASTIC QUANTIZATION AND ITO-STRATONOVICH RELATED INTERPRETATION

H NAKAZATO, K OKANO, L SCHULKE, Y YAMANAKA

NUCLEAR PHYSICS B   346 ( 2-3 ) 611 - 631  1990.12  [Refereed]

• THERMODYNAMICS AND QUANTUM-FIELD THEORY

HARDMAN, I, H UMEZAWA, Y YAMANAKA

PHYSICS LETTERS A   146 ( 6 ) 293 - 298  1990.06  [Refereed]

• DISSIPATION OF INTERACTING FIELDS IN THE PRESENCE OF BLACK-HOLES

AEI JOHANSSON, H UMEZAWA, Y YAMANAKA

CLASSICAL AND QUANTUM GRAVITY   7 ( 3 ) 385 - 390  1990.03  [Refereed]

• COHERENT AND THERMAL COHERENT STATE

A MANN, M REVZEN, K NAKAMURA, H UMEZAWA, Y YAMANAKA

JOURNAL OF MATHEMATICAL PHYSICS   30 ( 12 ) 2883 - 2890  1989.12  [Refereed]

16
Citation
(Scopus)
• RELATION BETWEEN QUANTUM AND THERMAL FLUCTUATIONS

A MANN, M REVZEN, H UMEZAWA, Y YAMANAKA

PHYSICS LETTERS A   140 ( 9 ) 475 - 478  1989.10  [Refereed]

• SELF-CONSISTENT RENORMALIZATION IN THERMOFIELD DYNAMICS

H UMEZAWA, Y YAMANAKA

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL   22 ( 13 ) 2461 - 2473  1989.07  [Refereed]

• SELF-CONSISTENT ANALYSIS OF A THERMALLY DISSIPATIVE QUANTUM-FIELD SYSTEM - KORENMAN MODEL

HARDMAN, I, H UMEZAWA, Y YAMANAKA

PHYSICA A   156 ( 3 ) 853 - 875  1989.04  [Refereed]

• ONE-LOOP CALCULATION IN TIME-DEPENDENT NON-EQUILIBRIUM THERMO FIELD-DYNAMICS

H UMEZAWA, Y YAMANAKA

FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS   37 ( 11 ) 819 - 837  1989  [Refereed]

2
Citation
(Scopus)
• LINEAR RESPONSE IN NON-EQUILIBRIUM THERMO FIELD-DYNAMICS

K NAKAMURA, Y YAMANAKA, H UMEZAWA

PHYSICA A   152 ( 1-2 ) 29 - 50  1988.09  [Refereed]

• MICRO, MACRO AND THERMAL CONCEPTS IN QUANTUM-FIELD THEORY

H UMEZAWA, Y YAMANAKA

ADVANCES IN PHYSICS   37 ( 5 ) 531 - 557  1988.09  [Refereed]

74
Citation
(Scopus)
• CALCULATION OF BETA-FUNCTIONS UP TO 2-LOOP ORDER IN PHI-4 THEORY BASED ON STOCHASTIC QUANTIZATION METHOD

H NAKAZATO, G TAKADA, H SOSHI, Y YAMANAKA

PROGRESS OF THEORETICAL PHYSICS   80 ( 3 ) 559 - 565  1988.09  [Refereed]

• SPATIALLY INHOMOGENEOUS THERMO FIELD-DYNAMICS

K NAKAMURA, H UMEZAWA, Y YAMANAKA

PHYSICA A   150 ( 1 ) 118 - 136  1988.05  [Refereed]

• SPONTANEOUS CREATION OF DISSIPATION IN THERMO FIELD-DYNAMICS AND ITS EXAMPLES

T ARIMITSU, H UMEZAWA, Y YAMANAKA, NJ PAPASTAMATIOU

PHYSICA A   148 ( 1-2 ) 27 - 45  1988.02  [Refereed]

• TIME-DEPENDENT CANONICAL FORMALISM OF THERMALLY DISSIPATIVE FIELDS AND RENORMALIZATION SCHEME

HARDMAN, I, H UMEZAWA, Y YAMANAKA

JOURNAL OF MATHEMATICAL PHYSICS   28 ( 12 ) 2925 - 2938  1987.12  [Refereed]

30
Citation
(Scopus)
• CANONICAL FORMALISM OF DISSIPATIVE FIELDS IN THERMO FIELD-DYNAMICS

T ARIMITSU, H UMEZAWA, Y YAMANAKA

JOURNAL OF MATHEMATICAL PHYSICS   28 ( 11 ) 2741 - 2752  1987.11  [Refereed]

32
Citation
(Scopus)
• The Thermally Dissipative Free Field and Canonical Formalism

H., Umezawa, Y., Yamanaka, I., Hardman, T., Arimitsu

Wondering in the Fields     174-190  1987.01  [Refereed]

• MINKOWSKI STOCHASTIC QUANTIZATION

H NAKAZATO, Y YAMANAKA

PHYSICAL REVIEW D   34 ( 2 ) 492 - 496  1986.07  [Refereed]

26
Citation
(Scopus)
• COMPLETE RENORMALIZATION SCHEME FOR FICTITIOUS-TIME CORRELATIONS IN STOCHASTIC QUANTIZATION METHOD BASED ON OPERATOR-FORMALISM

M NAMIKI, Y YAMANAKA

PROGRESS OF THEORETICAL PHYSICS   75 ( 6 ) 1447 - 1459  1986.06  [Refereed]

• POSSIBLE NONVANISHING MASS OF PHOTON

H NAKAZATO, M NAMIKI, Y YAMANAKA, K YOKOYAMA

PROGRESS OF THEORETICAL PHYSICS   75 ( 3 ) 686 - 691  1986.03  [Refereed]

• MASSIVE ABELIAN GAUGE-FIELDS COUPLED WITH NONCONSERVED CURRENTS - RENORMALIZATION SCHEME

H NAKAZATO, M NAMIKI, Y YAMANAKA, K YOKOYAMA

PROGRESS OF THEORETICAL PHYSICS   75 ( 1 ) 175 - 191  1986.01  [Refereed]

• SELF-REGULARIZED FIELD-THEORY AND ITS RENORMALIZATION IN MODIFIED STOCHASTIC QUANTIZATION

M NAMIKI, Y YAMANAKA

HADRONIC JOURNAL   7 ( 3 ) 594 - 640  1984  [Refereed]

• NEUTRINO MASSES, MIXING, AND OSCILLATIONS IN THE S4 MODEL OF PERMUTATION SYMMETRY

T BROWN, S PAKVASA, H SUGAWARA, Y YAMANAKA

PHYSICAL REVIEW D   30 ( 1 ) 255 - 257  1984  [Refereed]

52
Citation
(Scopus)
• PHENOMENOLOGICAL ANALYSIS OF Z0-]LL-GAMMA DECAY ON EXCITED LEPTON HYPOTHESIS

H NAKAZATO, M NAMIKI, Y YAMANAKA, K YOKOYAMA

PROGRESS OF THEORETICAL PHYSICS   72 ( 4 ) 865 - 868  1984  [Refereed]

• STOCHASTIC QUANTIZATION OF NON-ABELIAN GAUGE FIELD - UNITARITY PROBLEM AND FADDEEV-POPOV GHOST EFFECTS

M NAMIKI, OHBA, I, K OKANO, Y YAMANAKA

PROGRESS OF THEORETICAL PHYSICS   69 ( 5 ) 1580 - 1599  1983  [Refereed]

• STOCHASTIC QUANTIZATION METHOD OF FERMION FIELDS

T FUKAI, H NAKAZATO, OHBA, I, K OKANO, Y YAMANAKA

PROGRESS OF THEORETICAL PHYSICS   69 ( 5 ) 1600 - 1616  1983  [Refereed]

• STOCHASTIC QUANTIZATION METHOD IN OPERATOR-FORMALISM

M NAMIKI, Y YAMANAKA

PROGRESS OF THEORETICAL PHYSICS   69 ( 6 ) 1764 - 1793  1983  [Refereed]

• B-L AND NUCLEON DECAYS IN THE SUBQUARK MODEL

OHBA, I, Y YAMANAKA

PHYSICS LETTERS B   109 ( 5 ) 375 - 379  1982  [Refereed]

• PERMUTATION SYMMETRIES AND THE FERMION MASS MATRIX

Y YAMANAKA, H SUGAWARA, S PAKVASA

PHYSICAL REVIEW D   25 ( 7 ) 1895 - 1903  1982  [Refereed]

171
Citation
(Scopus)
• HIGH-ENERGY MANIFESTATIONS OF HEAVY QUARKS IN AXIAL-VECTOR NEUTRAL CURRENTS

Y KIZUKURI, OHBA, I, K OKANO, Y YAMANAKA

PHYSICAL REVIEW D   23 ( 9 ) 2095 - 2097  1981  [Refereed]

6
Citation
(Scopus)
• e+e- decay processes of cbar c bound states in relativistic harmonic oscillator model

Y. Kizukuri, K. Okano, Y. Yamanaka

Prog. Theor. Phys.   59   949 - 958  1978  [Refereed]

Books and Other Publications

• 「複雑系叢書 5 複雑さと法則」 「量子揺らぎ」

早稲田大学複雑系高等研究所

共立出版  2006.11

• ペレス 量子論の概念と手法

大場一郎, 山中由也, 中里弘道

丸善  2001.09

• Selected Papers of Hiroomi Umezawa

A. Arimitsu, H. Ezawa, H. Matsumoto, K. Nakamura, Y. Yamanaka

学習院大  2001.07

Misc

• 7aAW-2 Analysis of Quantum Transport Equation for Nonequilibrium Process in Ultracold Two-component Fermionic Gases

Imai Ryosukc, Nakamura Yusuke, Kuwahara Yukiro, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   69 ( 2 ) 53 - 53  2014.08

• 8aAW-12 Analysis on zero mode and phase fluctuation for Bose-Einstein condensate of confined cold atomic gas

Nakamura Yusuke, Takahashi Junichi, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   69 ( 2 ) 70 - 70  2014.08

• 27aCF-6 Relation between snake instability and zero mode of translational invariance for two-dimensional system with soliton

Takahashi Junichi, Nakamura Yusuke, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   69 ( 1 ) 171 - 171  2014.03

• 27aAD-7 Derivation of nonequilibrium Thermo Field Dynamics from classical Hamilton's principle with doubled degrees of freedom

Kuwahara Yukiro, Nakamura Yusuke, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   69 ( 1 ) 285 - 285  2014.03

• Relations between dynamical instability and zero modes for dark soliton in Bose-Einstein condensate

Takahashi Junichi, Nakamura Yusuke, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   68 ( 2 ) 137 - 137  2013.08

• 29pEE-4 Analysis for diffusion of fermion by lattice oscillation confined with harmonic oscillator potential in three dimensional optical lattice

Inoue Motoyoshi, Nakamura Yusuke, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   68 ( 1 ) 248 - 248  2013.03

• 18aAL-11 Thermal relaxation process for Bose gases in one dimensional optical lattice with nonequilibrium Thermo Field Dynamics

Kuwahara Yukiro, Nakamura Yusuke, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   67 ( 2 ) 127 - 127  2012.08

• 19aPSB-27 The roles of the two zero and adjoint modes in the dynamics of dark soliton

Takahashi Junichi, Nakamura Yusuke, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   67 ( 2 ) 261 - 261  2012.08

• 20aAL-2 Thermal relaxation process of the nonequilibrium initial distribution for s=1/2 Fermi gas in nonequilibrium Thermo Field Dynamics

Nakamura Yusuke, Kuwahara Yukiro, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   67 ( 2 ) 165 - 165  2012.08

• 24pAD-6 Analysis with Gutzwiller anzatz for Mott insulator transition of cold fermion gas in optical lattice system

Inoue Motoyoshi, Nakamura Yusuke, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   67 ( 1 ) 187 - 187  2012.03

• 26aTE-6 Extension of Nelson's Stochastic Quantization to Finite Temperature in Thermo Field Dynamics

Kobayashi Keita, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   65 ( 2 ) 295 - 295  2010.08

• 26aRD-10 Effect of finite temperature on superfluid-Mott insulator transition in pseudo one dimension

Inoue Motoyoshi, Kobayashi Keita, Nakamura Yusuke, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   65 ( 2 ) 162 - 162  2010.08

• 21pTB-12 Quantum transport equation for condensed system of cold atoms with time-dependent order parameter in non-equilibrium Thermo Field Dynamics

Nakamura Yusuke, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   65 ( 1 ) 190 - 190  2010.03

• 20aTB-10 Effect of trapping potential on superfluid-Mott insulator transition in pseudo one dimension

Inoue Motoyoshi, Kobayashi Keita, Nakamura Yusuke, Yamada Yukihiro, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   65 ( 1 ) 159 - 159  2010.03

• 25aZE-13 Analysis on the multi-component Bose-Einstein Condensation including Zero-Modes

Mine Makoto, Kobayashi Keita, Takei Ikuo, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   64 ( 2 ) 54 - 54  2009.08

• 29pSK-13 Derivation of Quantum Boltzmann Equations for Systems of Cold Atoms in a Framework of Nonequilibrium Thermo Field Dynamics

Nakamura Yusuke, Sunaka Tomoka, Mine Makoto, Okumura Masahiko, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   64 ( 1 ) 171 - 171  2009.03

• 21aZD-10 Analytical description of decay of a highly quantized vortex in Bose condensates

Kobayashi Keita, Nakamura Yusuke, Mine Makoto, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   63 ( 2 ) 115 - 115  2008.08

• 21pRG-12 Quantum Field Theoretical Analysis on Dynamical Instability of Bose-Einstein Condensates in Optical Lattices

Kobayashi Keita, Mine Makoto, Okumura Masahiko, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   62 ( 2 ) 162 - 162  2007.08

• 21pRG-13 Analysis on the Condition of the Existence of Complex Eigenvalues in Bogoloiubov-de Gennes Equations

Nakamura Yusuke, Mine Makoto, Okumura Masahiko, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   62 ( 2 ) 162 - 162  2007.08

• 18aXJ-10 Relation between two "diagonalization methods of Hamiltonian" of trapped Bose gas with complex eigenmodes

Mine Makoto, Okumura Masahiko, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   62 ( 1 ) 119 - 119  2007.02

• 23pRB-9 The Condition for Existence of Comlex Modes in Trapped Bose-Einstein Condensate with a Highly Quantized Vortex

SUNAGA Tomoka, FUKUYAMA Eriko, MINE Makoto, OKUMURA Masahiko, YAMANAKA Yoshiya

Meeting abstracts of the Physical Society of Japan   61 ( 2 ) 89 - 89  2006.08

• 28aRE-2 Many-Body Effects in Potential Scattering Problem with Time-Dependent Gross-Pitaevskii Equation 2

FUJISHIMA Hironobu, MINE Makoto, OKUMURA Masahiko, YAMANAKA Yoshiya

Meeting abstracts of the Physical Society of Japan   61 ( 1 ) 148 - 148  2006.03

• 27aSA-2 Diagonal representation of Hamiltonian with complex eigenvalue for Bose-Einstein condensation in optical lattice

Kobayashi Keita, Mine Makoto, Okumura Masahiko, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   61 ( 1 ) 131 - 131  2006.03

• 19pYA-12 Bogoliubov-de Gennes Approach with Complex Energy Modes and Quasi-Particle Picture

Mine Makoto, Okumura Masahiko, Sunaga Tomoka, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   60 ( 2 ) 54 - 54  2005.08

• 25aYE-5 Quantum Field Theoretical Formulation of Trapped Bose-Einstein Condensate with Vortex Including Zero-Mode

SUNAGA Tomoka, MINE Makoto, OKUMURA Masahiko, YAMANAKA Yoshiya

Meeting abstracts of the Physical Society of Japan   60 ( 1 ) 142 - 142  2005.03

• 24aYA-4 Relationship between Hugenholtz-Pines theorem and Ward-Takahashi identity in a homogeneous Bose gas

Enomoto H., Okumura M., Yamanaka Y.

Meeting abstracts of the Physical Society of Japan   60 ( 1 ) 133 - 133  2005.03

• 12aTF-11 Effect of Zero-Mode on Response of Trapped Bose-Condensed Atoms

Mine Makoto, Koide Tomoi, Okumura Masahiko, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   59 ( 2 ) 91 - 91  2004.08

• Renormalization condition of self-energy in trapped Bose-Eiustein condensate

Okumura M., Yamanaka Y.

Meeting abstracts of the Physical Society of Japan   58 ( 1 ) 159 - 159  2003.03

• Analysis of Response of Trapped Atomic Bose-Einstein Condensates under External Perturbation

Koide Tomoi, Mine Makoto, Okumura Masahiko, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   58 ( 1 ) 159 - 159  2003.03

• Response of Trapped Atomic Base-Einstein Condensates under External Perturbation

Koide Tomoi, Mine Makoto, Okumura Masahiko, Yamanaka Yoshiya

Meeting abstracts of the Physical Society of Japan   57 ( 2 ) 127 - 127  2002.08

• 奥村 雅彦, 山中 由也

物性研究   78 ( 3 ) 247 - 249  2002

• 26aA-4 A description of Bose-Einstein condensation in a harmonic potencial by quantum field theory

Okumura M, Yamanaka Y

Meeting abstracts of the Physical Society of Japan   54 ( 2 ) 116 - 116  1999.09

• 今福 健太郎, 大場 一郎, 山中 由也

早稲田大学情報科学研究教育センタ-紀要   ( 21 ) 41 - 50  1997.03

• 今福 健太郎, 大場 一郎, 山中 由也

物性研究   66 ( 2 ) 312 - 325  1996

View Summary

Nelson流の実時間確率過程量子化法をもちいたトンネル現象の解析を行う。Nelson流のアプローチは各試行毎の記述を探る可能性をもつものであり、量子力学に新しい視点を与えている。我々は、このアプローチを用いていわゆるトンネル時間を定義し、簡単な場合について数値計算による定量的解析を行った。

• 27p-X-6 Tunneling Time and Nelson's Quantization Method with Channel Coupling

Imafuku Kentaro, Ohba Ichiro, Yamanaka Yoshiya

Abstracts of the meeting of the Physical Society of Japan. Sectional meeting   1995 ( 2 ) 139 - 139  1995.09

• Tunneling Time with Bohm-Nelson stochastic mechanics

Imafuku K, Ohba I, Yamanaka Y

Abstracts of the meeting of the Physical Society of Japan. Annual meeting   50 ( 2 ) 207 - 207  1995.03

Research Projects

• Formulation of quantum fluctuation of zero mode in inhomogeneous systems and its applications to cold atomic systems and nuclei

Project Year :

2016.04
-
2019.03

View Summary

The zero mode associated with a spontaneous breakdown of a continuous symmetry plays a crucial role.Its quantum fluctuations have not been taken account of explicitly for infinite homogeneous systems.But it is not the case for finite inhomogeneous systems, for which a new consistent formulation to include zero mode fluctuations explicitly has been proposed recently. In this study, we apply it to cold stomic systems and nuclear systems descibed by the alpha cluster model, and to analyze physical effects of quantum fluctuations of the zero modes qunatitatively. The results can be tested experimentally

• Quantum transport equation snd its application to ultracold atomic system

Project Year :

2013.04
-
2016.03

View Summary

We derived the quantum transport equations for ultracold atomic systems without condensate from the formulation of nonequilibrium processes based on quantum field theory, and solved them numerically. It is shown that the imaginary part in the self-energy is essential for relaxation of the system to equilibrium, and that the non-Markoffian property decelerate nonequilibrium processes.In order to describe a nonequilibrium process involving condensation, we have established a new formulation of zero modes associated with a spontaneous breakdown of symmetry for a finite-size systems, for which the conventional Bogoliubov approximation is legitimate. The new formulation is applied to a system of a dark soliton in a condensate, or to the alpha-cluster model in nuclear physics, giving us new interpretations of the phenomena

• Quantum transport equation snd its application to ultracold atomic system

Project Year :

2013
-
2015

View Summary

We derived the quantum transport equations for ultracold atomic systems without condensate from the formulation of nonequilibrium processes based on quantum field theory, and solved them numerically. It is shown that the imaginary part in the self-energy is essential for relaxation of the system to equilibrium, and that the non-Markoffian property decelerate nonequilibrium processes.In order to describe a nonequilibrium process involving condensation, we have established a new formulation of zero modes associated with a spontaneous breakdown of symmetry for a finite-size systems, for which the conventional Bogoliubov approximation is legitimate. The new formulation is applied to a system of a dark soliton in a condensate, or to the alpha-cluster model in nuclear physics, giving us new interpretations of the phenomena

• Research on Quantum Field Theory for Finite Space-Time Systems and Dynamics of Quantum Systems

View Summary

In this project the head investigator, I. Ohba together with Y. Ota quantized the dissipative chaos system applying the method of stochastic state diffusion, and discussed the quantum-classical correspondence quantitatively calculating pseudo-Lyapunov index. Then they developed the semiclassical approximation on the quantum dissipative system. Further, they focused on the quantum computer of nuclear spins in a semiconductor proposed by B. E. Kane, and solved the time-dependent Schrodinger equation rigorously and showed that the inevitable operation error exists in the previously proposed way of construction of the quantum gates.H. Nakazato and K. Yuasa reconsidered the quantum Zeno effect including the degrees of freedom of the environment, and found that the "environment" (of finite degrees of freedom)is purified by the Zeno-like measurement in which the frequent sequential measurements are performed on the system. As an application, they showed that the entanglement distillation and initialization of qubits are possible. Further, they developed the method to derive the solution of Lindlbad master equation with the Kraus representation.Y. Yamanaka together with one of the members M. Okumura considered the system of Bose-Einstein condensation of atomic gas where the translational invariance is absent due to the trapping potential for atoms, and developed its quantum field theoretical formulation. They also showed that inclusion of Goldstone mode is essential in this framework. Particularly, this formulation keeps the Ward-Takahashi identities and the degenerated vacuum is orthogonal to each other.Y. Yamanaka, M. Okumura and M. Mine showed the relation between two kinds of field theoretical methods in which the Goldstone mode is taken care of for a trapped Bose-condensed system. Further, they formulated the method in which the effect of the zero-mode on the response of trapped Bose-Einstein condensates against the external perturbation at finite temperature can be evaluated. Using this formalism, they numerically calculated its effects

• Formulation of Bose-Einstein condensation of neutral atoms based on thermal field theory

Specific Research

• 2019   高橋　淳一, 大山　京尋

View Summary

非一様有限系の自発的対称性の破れに伴って現れるゼロモードはその量子揺らぎが無視できない。場の量子論で厳格に定式化する方法として、非摂動ハミルトニアンに非線形ゼロモード項を取り入れることを提唱してきたが、αクラスター構造原子核でα粒子が凝縮している場合の理論的研究を行った。2019年度の最大の成果として、そうした系は超流動状態と規則的格子状態とが共存する超固体描像で解釈できるということを見出した。この成果はProg.Theor. Exp. Phys. (S. Ohkubo, J. Takahashi, Y. Yamanaka), "Supersolidity of $\alpha$ cluster structure in the nucleus 12C")に掲載決定された。

• 2011   中村　祐介, 井上　智喜

View Summary

本研究課題の目的は、量子多体系の基礎理論である場の量子論に基づいて、非平衡過程を記述する熱場の量子論の構築にある。冷却原子系は、(1) 希薄で粒子間の相互作用が通常小さく実験と理論の直接比較を可能、(2) 多数の実験パラメーターが制御可能である、(3) 様々なゆっくり進行する非平衡過程が実現可能、(4) ボソン系のBose-Einstein凝縮相と非凝縮相間の転移や光学格子中の超流動－Mott絶縁体転移などの様々な相転移の存在、などの理由によりそうした理論の構築・検証に現在最適な系である。熱場の量子論の形式としては、Thermo Field Dynamics（TFD）を用いる。この方向の研究として既に冷却ボース原子気体系に対して、統一的観点から非平衡TFDの定式化を行った（Y. Nakamura and Y. Yamanaka, Ann. Phys. Vol. 326, 1070 （2011年4月）)が、本研究ではさらに我々の用いるTFDと多くの物理学者が研究で用いているClosed Time Path法との相違を明らかにした。最も重要な相違点は、非平衡TFDでは粒子描像が時間と共に変わることに対応していることとGreen関数においてマクロな量に関して時間の矢の向きの因果律を満たしていることである。この研究成果は二つの研究会での招待講演（京都大学基礎物理学研究所　「熱場の量子論とその応用」　2011年8月　会議録は論文１、理化学研究所　「重イオン衝突と非平衡物理の理論的発展」　2012年2月）で発表した。　非平衡TFDに関連した研究として、相対論的中性スカラー場に対しても我々の方法を拡張して、量子輸送方程式が導かれることを示した（論文２）。この成果は重イオン衝突のクォーク・グルーオンプラズマや宇宙初期の非平衡過程の研究に役立つものである。　平衡系の冷却原子系の分野では、光学格子中の冷却原子系をBose-Hubbardモデルを用いて、Mott絶縁体－超流動に関わる有限温度における相図の研究を行った（論文３）。これはMott絶縁体－超流動相転移の非平衡過程を扱う準備となる。

• 2010

View Summary

量子多体系の基礎理論である場の量子論に基づいて、非平衡過程を記述する熱場の量子論の構築することを目的に、近年実験的・理論的研究が盛んな冷却中性原子気体系を対象として研究を行っている。この冷却原子系では、様々な観測可能な非平衡過程が実現されているからである。熱場の量子論の方法論としては実時間正準場の理論形式であるThermo Field Dynamics (TFD)を用いる。　研究成果として、冷却ボース中性原子気体系に対して、統一的観点から非平衡TFDの定式化を行った。具体的には、ボース・アインシュタイン凝縮体が存在しない場合、時間に依存しない凝縮体が存在する場合、最後に時間に依存する凝縮体が存在する場合、それぞれにループ計算結果に非平衡TFDにおける繰り込み条件を課すことで重要な結果を導いた。特に、時間に依存する凝縮体が存在する場合に、この系の時間発展を記述する３組の連立方程式、すなわち、運動学的方程式、秩序パラメータを記述する時間依存Gross-Pitaevskii方程式、励起状態を記述する時間依存Bogoliubov-de Gennes方程式を導出した。これらの方程式が単なる現象論的な組み合わせではなく、場の量子論に忠実な立場で自己無撞着に導出されていることが重要な点である。さらに得られた運動学的方程式を数値的に解き、凝縮体が安定な場合・不安定な場合における挙動を定性的に評価した。

• 2009

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1995年、冷却中性原子気体系においてBose-Einstein凝縮（以下BEC）が実現された。盛んに実験及び理論研究がなされている外部ポテンシャルにより閉じ込められた冷却中性原子系は、希薄で相互作用が弱いこと、様々な実験パラメータの制御性の高さなどから、量子多体系の基礎の検証、特に非平衡過程を記述する熱場の量子論の構築に最適な系である。従来の冷却原子系に対する理論的解析においては、平均場、あるいは平均場のまわりの線形励起を加えた理論が圧倒的多数であるが、本研究では熱的及び量子揺らぎ効果を原理的に完全に取り入れた実時間正準形式熱場の量子論であるThermo Field Dynamics（以下TFD）を採用している。非平衡TFDの既存の研究で、空間一様系、あるいは終状態が空間一様平衡状態になる拡散系に限って、場の量子論の自己無撞着繰り込み条件から、時間依存粒子数分布に対する運動学的方程式が導かれるている。今年度発表した成果として、並進対称性のない有限サイズ系である閉じ込められた冷却原子気体系を対象に、BECのない場合と時間依存しないBECの場合に、非平衡TFD形式で場の量子論の自己無撞着繰り込み条件から、時間依存粒子数分布に対する運動学的方程式を導いた。この研究の重要な点は、場の量子論として正しい準粒子描像に基づいていることである。2-ループレベルでBECのない場合導かれた非マルコフ運動学的方程式は、マルコフ極限で、他の方法でも導かれている量子Boltzmann方程式に一致している。BECの存在する場合に導かれた方程式には、凝縮体から3粒子が生成される現象に対応する新しい衝突項が現れる。これは正しい準粒子描像に基づく結果である。この項の寄与は通常エネルギー保存則から禁止されているが、負エネルギー励起の現れるLandau不安定現象では重要となる。この研究はAnn. Phys.に論文として発表した。さらに、BECが時間依存する場合への拡張を試みており、一部成果を2010年3月日本物理学会にて発表した。

• 2004

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閉じ込められた中性原子のボースアインシュタイン凝縮系を(熱)場の量子論の立場から解析し、実験と比較をしながら、その理論形式を検証するこを目的をとして研究を行ってきた。特に、この系はトラップが存在し、並進対称性がない場合の大域位相対称性の自発的破れ現象と理解されるが、その機構の解明と検証が重要である。並進対称性のある場合と同様、Goldstoneの定理により、自発対称性の破れに伴い南部-Goldstoneモードが存在する。実際、離散ゼロ・モードを非摂動理論に取り入れなければ、場の量子論の基本的要請である正準交換関係を破ってしまうことが指摘されている。　今回の研究論文（M. Okumura and Y. Yamanaka, Physica A348 (2005) 157-172）では、ゼロ温度ツリー近似で知られているWard-高橋関係式の成立を、有限温度・ツリー近似でも、成立することを証明した。有限温度の場の理論形式としては、実時間演算式形式で今回のような厳密な場の量子論の議論に適したThermo Field Dynamicsを採用した。　こうした証明を通じて、ゼロ・モードを含む正しい準粒子描像を採用することが本質的であることを明らかにした。正準交換関係と矛盾しないゼロ・モードの導入の方法には、一般化されたBogoliubov変換法とBogoliubov-de Gennes法の2つのやり方が知られているが、前者に従って調べた。一般化されたBogoliubov変換法ではゼロ・モードに付随した赤外発散が現れるが、一方でその赤外発散の微妙な振る舞いが今回のWard-高橋関係式を保証していることを具体的に示した。　このようにWard-高橋関係式が成立することは、準粒子描像で導入されたゼロ・モードがGoldstoneの定理が要求する南部-Goldstoneモードになっていることを意味している。

• 2003

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近年実現されている中性アルカリ原子のBose-Einstein凝縮（以下BECと略記）状態生成実験に対して、我々が最も注目するのは、量子多体系を記述する基礎理論の検証の場としての条件を有している事実である。これまで、このBECの実験との比較は、Gross-Pitaevskii方程式(平均場近似)を用いる方法、あるいはそれに加えて励起状態を量子論的に扱うHartree-Fock-Bogoliubov)の方法などで行われているのが実情である。本研究では、この系を最も基礎的理論である場の量子論、さらにそれに熱的自由度を加えた熱場の量子論の立場から定式化し、量子多体系を記述する場の量子論や熱場の量子論の理論形式の検証を行うことを最終目標とする。BEC系で重要なの、自発的対称性の破れに伴い出現する南部-Goldstone（NG）モードである。場の理論の立場から言えば、NGモードを正しく取り扱わなければ、場の量子論で基本的関係である正準交換関係を破ってしまう。また、BECでの新しい点として、トラップの存在のために並進対称性がないことで、NGモードは離散スペクトルとして存在する。　BECで正準交換関係と矛盾しないようにNGモードを導入するには、2通りの方法が知られている。一つは(A)一般化されたBogoliubov形式で他の励起状態と同じように扱う方法と(B) Bogoliubov-de Gennes形式で量子座標として扱う方法である。(A)について場の量子論の定式化をして、密度分布関数に対する量子・熱揺らぎ効果をループ展開で計算した論文を（M. Okumura and Y. Yamanaka, Phys.Rev.A68 (2003) 013609）発表した。今回は(B)について同様に場の量子論として定式化した上でループ計算を実行し、その成果をまとめた（M. Okumura and Y. Yamanaka, Prog. Theor. Phys. 111 (2004) 199）。また、(A)と(B)の同等性についての証明を、論文としてまとめている。（M. Mine, M. Okumura and Y. Yamanaka, 投稿中）

• 1998

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1995年に始まるアルカリ原子のボース・アインシュタイン凝縮状態の実験は、近年の物理学最大の話題である。温度数百nKオーダーの純粋な凝縮系を実験室で自由に細工できることは、微視的世界の理論研究に重要な意義を有する。現在この凝縮状態の実験との比較は、Gross-Pitaevskii方程式（平均場近似）というc-数理論が主流で行われている。大雑把な性質は矛盾していないが、今後予想される詳細な実験では、とりわけ凝縮系が力学的に変化する様子を測定できるようになれば、より精密な量子効果を充分取り入れた理論による解析が必要である。　本研究は今後の精密実験に備えて、c-数理論ではなく、可能な限り量子効果を取り込んだ場の理論の立場から、問題の定式化を始めた。問題は、調和振動ポテンシャルが外力として存在する、自己相互作用するボース場（アルカリ原子を記述する）の系である。自己相互作用の結合定数gは小さいとは言え、凝縮生成には無視できない。今回は、粒子の総数Nが充分大きいとして、gNの項のみを残し、それ以上のg及びNの高次項を無視する近似で、Bogoliubov変換とコヒーレント変換を組み合わせて、ハミルトニアンを対角化できることを示した。その結果、例えば粒子分布関数が具体的に計算され、基底状態に関しても、荒い近似で通常仮定されるガウス型分布から定量的にかなりずれる（特に中心付近で大きくくぼむ）ことが明らかになった。この成果は、"5th International Workshop on Thermal Field Theories and Their Applications"(Regensburg August 1998)で報告した。　今後、熱的自由度を含むよう、上の定式化をThermo Field Dynamics という熱場の理論の枠組に乗せ、アルカリ原子のボース・アインシュタイン凝縮の熱的非平衡系研究に発展させる予定である。

• 1996

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本研究は巨視的な系と相互作用する量子系の振る舞いを、様々な角度から、特に新しい観点と方法を駆使して、理論定式化を目指したものである。今年度の成果は以下の通りである。　先ず、トンネル時間の評価に関して、昨年度Nelson流量子化によるトンネル現象の我々の新しい取り扱い(Phys.Lett. A204 (1995)329)を提唱した。今年度は、その適応範囲を広げるよた。現実の実験では、多数のチャンネルが結合している結果、非弾性過程が起こる。当然この非弾性効果はトンネル時間の評価にも影響するはずである。これまで多チャンネルが結合する系に対して、Nelson量子化での取り扱いは知られていなかった。今回、チャンネル間の量子飛躍を確率的飛躍過程とみなして、矛盾なく多チャンネル結合系に対してNelson流量子化を定式化することに成功した。さらにそれに基づいてトンネル時間を確率過程の数値計算で評価した。成果は論文に纏めて投稿中である。　量子力学の観測過程は通常、量子系と巨視系の相互作用によってもたらされると考えられている。今回我々が調べた問題は、ケーオス的振る舞いをする古典少数系と量子系との相互作用によって、量子系の位相相関が果たして切れるのかどうかということであった。古典少数系の動きが量子系に比べて著しく遅い場合と速い場合を調べ、我々の予想通り、条件次第で量子相関は切れることがあることが示せた(Phys. Lett. A222 (1996)130)。このことは、測定装置は必ずしも巨視的物理系でなければならないわけでなく、ケーオス的振る舞いをする少数系でも可能であるということで、今後の測定器の考案や観測問題では重要な指摘になっている。

• 1995

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現在の実験技術の向上は，量子系の微視的な波動関数（量子状態）のかなり詳細な形に依存する現象を実験対象にすることを可能にしている。本研究では，量子力学系と場の量子論系につき，以下の波動関数（量子状態）の動的振る舞いに関する理論研究を行った。（1）量子力学系で，粒子がポテンシャル障壁を「トンネリングするのに要する時間」（トンネリング時間）の問題は，古くから様々な物理学者によって提案されているが，いまだ決着されていない。問題の難しさは，トンネリングが純粋に量子論効果で古典的対応物がないことと，量子力学では時間変数が演算子で表せられる力学量でないことに起因する。我々はこの問題を新しい観点から論ずる方法として，Nelson流の確率過程量子化法でサンプルパスを考え，それからトンネリング時間を定義することを提案し，発表した（Physics Letters A）。この方法を用いて，トンネリング時間が，波束の形に依存する「躊躇時間」と「相互作用時間」の和であることが明らかにされた。初期波束の大きさなどをパラメータにして，これらの時間の数値解析の結果も具体的に得られている。（2）熱的状況にある場の量子論は，素粒子，宇宙論から物性物理に渡る広範な物理現象に関わる。当然，系の動的振る舞いも場の量子論に基づいて記述されなければならないが，非平衡系では確立された理論形式は未だ存在しない。TFD（Thermo Field Dynamics）を用いた熱的状況にある場の量子論系のこれまで行われてきた研究の一環として，空間不均一な場合の理論形式を整えた。それを自己相互作用する模型に適用し，空間勾配の低次の近似として粒子密度・エネルギー密度に対する拡散型方程式を導き，方程式に現れる諸パラメータを場の理論で計算する表式を示した。これらの結果は，熱的場の量子論の国際会議（4th International Workshop onThermal Field Theories and Their Applications, 大連）にて報告した。

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