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Progress of Theoretical Physics

Thermal Effects and Dissipation in su(1, 1)-Algebraic Model by Means of Time-Dependent Variational Approach

Y. Tsue, A. Kuriyama, M. Yamamura

Published Mar 1, 1994• 9 citations
Publisher

Abstract

The appearance of thermal effects is investigated in a simple system composed of quantum mechanical damped harmonic oscillator governed by su(1, 1)-algebra within a framework of the time-dependent variational approach in terms of mixed-mode coherent states. It is shown that certain fluctuations originated from the use of the mixed-mode coherent state can be interpreted as thermal fluctuations which appear in the form of the bose distribution function. Thus, our time-dependent variational approach with mixed-mode coherent states leads to a possible simultaneous description of classical motions and thermal fluctuations. It is also shown that the energy concentrated in a pure state at initial time dissipates to the other states after time-evolution. It is then remarked that the thermal effects play a significant role in the above process.

DOI
10.1143/ptp/91.3.469

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The appearance of thermal effects is investigated in a simple system composed of quantum mechanical damped harmonic oscillator governed by su(1, 1)-algebra within a framework of the time-dependent variational approach in terms of mixed-mode coherent states. It is shown that certain fluctuations originated from the use of the mixed-mode coherent state can be interpreted as thermal fluctuations which appear in the form of the bose distribution function. Thus, our time-dependent variational approach with mixed-mode coherent states leads to a possible simultaneous description of classical motions and thermal fluctuations. It is also shown that the energy concentrated in a pure state at initial time dissipates to the other states after time-evolution. It is then remarked that the thermal effects play a significant role in the above process.
The appearance of thermal effects is investigated in a simple system composed of quantum mechanical damped harmonic oscillator governed by su(1, 1)-algebra within a framework of the time-dependent variational approach in terms of mixed-mode coherent states. It is shown that certain fluctuations originated from the use of the mixed-mode coherent state can be interpreted as thermal fluctuations which appear in the form of the bose distribution function. Thus, our time-dependent variational approach with mixed-mode coherent states leads to a possible simultaneous description of classical motions and thermal fluctuations. It is also shown that the energy concentrated in a pure state at initial time dissipates to the other states after time-evolution. It is then remarked that the thermal effects play a significant role in the above process.
A time-dependent variational approach with a mixed-mode coherent state is applied to su(1, 1)-algebraic models derived from nuclear su(2)-models, which are the single orbit shell model with pairing correlation and the Lipkin model. The equations of motion are derived in a canonical form similar to that in the time-dependent Hartree-Fock theory, and the solutions are derived by the use of conserved action variables together with an appropriate canonical transformation. It is shown that thermal effects appear in the form of the bose distribution function. Also, it is found that the energy concentrated in a pure state at initial time dissipates to the other states in a manner similar to the case of the damped-and-amplified harmonic oscillator model investigated in our previous work.
A time-dependent variational approach with a mixed-mode coherent state is applied to su(1, 1)-algebraic models derived from nuclear su(2)-models, which are the single orbit shell model with pairing correlation and the Lipkin model. The equations of motion are derived in a canonical form similar to that in the time-dependent Hartree-Fock theory, and the solutions are derived by the use of conserved action variables together with an appropriate canonical transformation. It is shown that thermal effects appear in the form of the bose distribution function. Also, it is found that the energy concentrated in a pure state at initial time dissipates to the other states in a manner similar to the case of the damped-and-amplified harmonic oscillator model investigated in our previous work.
The su(2)-algebraic model interacting with an environment is investigated from the viewpoint of treating a dissipative system. By using a time-dependent variational approach with a coherent state and with the help of the canonicity condition, the time-evolution of this quantum many-body system is described in terms of the canonical equations of motion in the classical mechanics. Then, it is shown that the su(1, 1)-algebra plays an essential role in treating this model. An exact solution with appropriate initial conditions is obtained in terms of Jacobi's elliptic function. The implications for the dissipative process are discussed.
To appear in those proceedings.OCR Output 'Invited talk presented by M. Y. at the conference on "Many-Body Physics", Coimbra, Portugal, mixed states in highly excited nucleus.5•°•7 been formulated as the Dirac canonical formalism with constraints in order to describe the time-dependent variational principle and thermo field dynamics.This theory has Fiolhais, have also developed a microscopic theory for mixed states based on both is investigated.4Two of the authors (M.Y. and A.K.), together with Providéncia and based on the thermo field dynamics and the variation of the thermodynamic potential the thermo field dynamicsz has progressed,3 and the relation between the treatments description of mixed states in many-fermion systems.}Also, the treatment based on For example, the thermal boson expansion theory has been studied in the microscopic various attempts to describe the systems in the excited states have been developed.particle physics.In the field of microscopic theory in nuclear many-body systems, in highly excited states, has been one of the interesting problems in quantum many-The theoretical study of systems in highly excited states, such as nucleus observed a correct classical counterpart is examined and explicitly constructed as "mixed-means of time-dependent variational procedure, a possible state which can offerIn order to investigate quantal systems governed by su(1,1)-algebra by
An SU(1,1) Lie algebraic formulation is presented for investigating the linear dissipative processes in quantum optical systems. The Liouville space formulation, thermo field dynamics, and the disentanglement theorem of SU(1,1) Lie algebra play essential roles in this formulation. In the Liouville space, the time-evolution equation for the state vector of a system is solved algebraically by using the decomposition formulas of SU(1,1) Lie algebra and the thermal state condition of thermo field dynamics. The presented formulation is used for investigating a dissipative nonlinear oscillator, the quantum mechanical model of phase modulation, and the photon echo in the localized electron–phonon system. This algebraic formulation gives a systematic treatment for investigating the phenomena in quantum optical systems.