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Invited talk at

The SU(1,1) algebra and dissipation

M. Yamamura, A. Kuriyama, Y. Tsue

Published Jan 1, 1993• 0 citations

Abstract

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

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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

A classical microscopic theory of mixed states has recently been formulated in order to deal with the theoretical description of nuclear phenomena observed in highly excited states. In this theory, which is here briefly reviewed, the degrees of freedom of real fermions are doubled by fictitious fermions, in the context of the formalism of thermofield dynamics. The requirement of static stability of the thermal state of equilibrium plays, in the theory, a relevant role. The possibility of constraining the dynamics of the fictitious degrees of freedom, in such a way as to eliminate spurious thermal excitations, is discussed. The concept of canonical collective variables for mixed states is analyzed. Boson expansions appropriate to describe collective excitations of hot quantal systems are introduced and their properties investigated. It is shown that thermal boson expansions based on the formalism of thermofield dynamics are free from formal inconsistencies which may be present in boson expansions derived by an ad hoc quantization of conventional thermal mean field theories. The formalism is applied to the Lipkin model, and the correlation energy of a hot system is discussed.

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.