Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Progress of Theoretical Physics

On the Hamiltonians Expressed in Terms of su(1, 1)-Generators for Describing Thermal Effects in Nuclear su(2)-Models

Y. Tsue, A. Kuriyama, M. Yamamura

Published Mar 1, 1995• 1 citation
Publisher

Abstract

In order to develop a previously proposed method to investigate thermal effects in quantum many-particle systems, basic ideas are formulated in more general systems obeying su(2)-algebra. It is shown that Hamiltonians of a single orbit shell model with pairing correlation, the Lipkin model, a symmetric rigid rotor model and an asymmetric rigid rotor model have almost the same structure, that is algebraic structure of su(1, 1), by the use of the Holstein-Primakoff boson representation for su(2)-algebra and so-called phase-space doubling introduced to study thermal phenomena. It is also discussed that the interaction term between intrinsic system and external environment approximately represents the interesting physical process in each system at finite temperature.

DOI
10.1143/ptp/93.3.541

Related papers

The Lipkin Model in Many-Fermion System as an Example of the su(1,1) ⊗ su(1,1)-Algebraic Model

Constança Providência, João da Providência, Y. Tsue +1 more

Following an idea, recently, proposed by the present authors for the two-level pairing model, the Lipkin model is reexamined. It is a natural generalization of the method already developed by the present authors with Kuriyama. This model is a schematic model for many-fermion systems and obeys the su(2)-algebra. It is shown that the use of the Schwinger boson representation, the model is expressed in terms of the su(1,1) ⊗ su(1,1)-algebra and with the aid of the MYT mapping method, it is disguised from the orginal form in terms of the Holstein-Primakoff representation. Further, under various coherent states, the classical counterparts are derived. It is concluded that the Lipkin model can be treated in the common ring as that of the two-level pairing model.

arXiv:nucl-th/0604023•Progress of Theoretical Physics•Jul 1, 2006•4 citations

A pseudo su(1,1)-algebraic deformation of the Cooper pair in the su(2)-algebraic many-fermion model

Y. Tsue, Constança Providência, João da Providência +1 more

A pseudo su(1,1)-algebra is formulated as a possible deformation of the Cooper pair in the su(2)-algebraic many-fermion system. With the aid of this algebra, it is possible to describe the behavior of individual fermions which are generated as the result of interaction with the external environment. The form presented in this paper is a generalization of a certain simple case developed recently by the authors. The basic idea follows the su(1,1) algebra in the Schwinger boson representation for treating energy transfer between the harmonic oscillator and the external environment. The Hamiltonian is given following the idea of phase space doubling in the thermo-field dynamics formalism, and the time-dependent variational method is applied to this Hamiltonian. Its trial state is constructed in the frame deformed from the BCS-Bogoliubov approach to superconductivity. Several numerical results are shown.

arXiv:1306.3282•Progress of Theoretical and Experimental Physics•Oct 18, 2013•0 citations

Modification of the Conventional Holstein-Primakoff Boson Representation for the su(1,1)-Algebra and Its Classical Counterpart

A. Kuriyama, João da Providência, Y. Tsue +1 more

In order to avoid unsatisfactory points of the conventional Holstein-Primakoff representation of the su(1,1)-algebra for the description of thermal effects in many-boson or oscillating systems, the conventional form is modified. The basic idea can be found in a possible canonical transformation from the conventional to the new form. Four forms are given, and with the aid of these modified forms, it is expected to describe, for example, fluctuations around a bose-condensed state.

Progress of Theoretical Physics•May 1, 1998•0 citations

Description of Thermal Effects in su(1, 1)-Algebraic Model Derived from Nuclear su(2)-Model

Y. Tsue, A. Kuriyama, Masatoshi Yamamura

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.

Progress of Theoretical Physics•Jun 1, 1995•0 citations

Description of Thermal Effects in su(1, 1)-Algebraic Model Derived from Nuclear su(2)-Model

Y. Tsue, A. Kuriyama, M. Yamamura

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.

Progress of Theoretical Physics•Jun 1, 1995•0 citations

The Lipkin Model in the su(M + 1)-Algebra for Many-Fermion System and Its Counterpart in the Schwinger Boson Representation

Constança Providência, João da Providência, Y. Tsue +1 more

Following the Schwinger boson representation for the su(M + 1)- and su(N, 1)-algebras presented by two of the present authors (J. da P. and M. Y.) and Kuriyama, a possible counterpart of the Lipkin model in the su(M + 1)-algebra formulated in the fermion space is presented. The free vacuum, which plays a fundamental role in the conventional treatment of the Lipkin model, is generalized in a quite natural way, and further, the excited state generating operators, such as the particle-hole pairs, are also given in a natural scheme. As concrete examples, the cases of the su(2)-, su(3)- and su(4)-algebras are studied. Especially, the case of the su(4)-algebra is investigated in detail in relation to the nucleon pairing correlations and the high-temperature superconductivity.

arXiv:nucl-th/0504024•Progress of Theoretical Physics•Jul 1, 2005•0 citations
In order to develop a previously proposed method to investigate thermal effects in quantum many-particle systems, basic ideas are formulated in more general systems obeying su(2)-algebra. It is shown that Hamiltonians of a single orbit shell model with pairing correlation, the Lipkin model, a symmetric rigid rotor model and an asymmetric rigid rotor model have almost the same structure, that is algebraic structure of su(1, 1), by the use of the Holstein-Primakoff boson representation for su(2)-algebra and so-called phase-space doubling introduced to study thermal phenomena. It is also discussed that the interaction term between intrinsic system and external environment approximately represents the interesting physical process in each system at finite temperature.
Following an idea, recently, proposed by the present authors for the two-level pairing model, the Lipkin model is reexamined. It is a natural generalization of the method already developed by the present authors with Kuriyama. This model is a schematic model for many-fermion systems and obeys the su(2)-algebra. It is shown that the use of the Schwinger boson representation, the model is expressed in terms of the su(1,1) ⊗ su(1,1)-algebra and with the aid of the MYT mapping method, it is disguised from the orginal form in terms of the Holstein-Primakoff representation. Further, under various coherent states, the classical counterparts are derived. It is concluded that the Lipkin model can be treated in the common ring as that of the two-level pairing model.
A pseudo su(1,1)-algebra is formulated as a possible deformation of the Cooper pair in the su(2)-algebraic many-fermion system. With the aid of this algebra, it is possible to describe the behavior of individual fermions which are generated as the result of interaction with the external environment. The form presented in this paper is a generalization of a certain simple case developed recently by the authors. The basic idea follows the su(1,1) algebra in the Schwinger boson representation for treating energy transfer between the harmonic oscillator and the external environment. The Hamiltonian is given following the idea of phase space doubling in the thermo-field dynamics formalism, and the time-dependent variational method is applied to this Hamiltonian. Its trial state is constructed in the frame deformed from the BCS-Bogoliubov approach to superconductivity. Several numerical results are shown.
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.
Following the Schwinger boson representation for the su(M + 1)- and su(N, 1)-algebras presented by two of the present authors (J. da P. and M. Y.) and Kuriyama, a possible counterpart of the Lipkin model in the su(M + 1)-algebra formulated in the fermion space is presented. The free vacuum, which plays a fundamental role in the conventional treatment of the Lipkin model, is generalized in a quite natural way, and further, the excited state generating operators, such as the particle-hole pairs, are also given in a natural scheme. As concrete examples, the cases of the su(2)-, su(3)- and su(4)-algebras are studied. Especially, the case of the su(4)-algebra is investigated in detail in relation to the nucleon pairing correlations and the high-temperature superconductivity.