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

Three Forms of Coherent States in the su(2)-Spin System and Related Classical Counterparts

A. Kuriyama, João da Providência, Y. Tsue, M. Yamamura

Published Aug 1, 1997• 3 citations
Publisher

Abstract

In terms of the boson coherent state and a possible extension, three forms of wave packets are presented in the Schwinger boson representation. Each wave packet gives classical counterpart for a certain set of operators, for example, three components of the su(2)-spin. Furthermore, uncertainty relations which come from the boson coherent state and its extension are examined. The content discussed in this paper is, in a certain sense, an extension of that discussed in a paper presented recently by the present authors.

DOI
10.1143/ptp.98.381

Related papers

Three Forms of Boson Expansions for the su(2)-Spin System and Their c-Number Counterparts

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

In the framework of the Marumori-Yamamura-Tokunaga boson expansion, three forms for the su(2)-spin system are presented. The first is related with the well-known Holstein-Primakoff boson expansion and the second is the expansion reinvestigated in a previous paper by the present authors. The third is, in some sense, the original part of this paper. Corresponding with three forms, c-number counterparts are obtained by using three forms of wave packets defined in the su(2)-spin space. With the help of appropriate quantization rule, they go back to the original boson expansions. Furthermore, it is discussed if the c-number counterparts can be regarded as the classical counterparts. Finally, the relation to the su(1, 1)-algebraic model is discussed.

Progress of Theoretical Physics•Aug 1, 1996•0 citations

A Possible Classical Description for su(1, 1)-Spin Systems

Y. Tsue, A. Kuriyama, M. Yamamura

With the aim of investigating dynamics of systems governed by su (1, 1)-algebra, a possible state which can give us a classical counterpart for the su (1, 1)-spin system properly is examined and constructed explicitly. By the use of canonicity conditions developed in the time-dependent Hartree-Fock theory, the c -number analogue of the Holstein-Primakoff boson representation is obtained for the su (1, 1)-algebra. It is noted that it is important to introduce a character of two-mode coherent state in order to present a suitable classical counterpart for the su (1, 1)-spin. Furthermore, it is shown that the spreading of uncertainty relations appears inevitably, which suggests that a certain fluctuation can be introduced.

Progress of Theoretical Physics•Jan 1, 1994•2 citations

A Possible Classical Description for su(1, 1)-Spin Systems

Y. Tsue, A. Kuriyama, Masatoshi Yamamura

With the aim of investigating dynamics of systems governed by su (1, 1)-algebra, a possible state which can give us a classical counterpart for the su (1, 1)-spin system properly is examined and constructed explicitly. By the use of canonicity conditions developed in the time-dependent Hartree-Fock theory, the c -number analogue of the Holstein-Primakoff boson representation is obtained for the su (1, 1)-algebra. It is noted that it is important to introduce a character of two-mode coherent state in order to present a suitable classical counterpart for the su (1, 1)-spin. Furthermore, it is shown that the spreading of uncertainty relations appears inevitably, which suggests that a certain fluctuation can be introduced.

Progress of Theoretical Physics•Jan 1, 1994•0 citations

Note on Boson Expansion and Boson Coherent State for the su(2)-Spin System

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

With the aim of obtaining the classical counterpart of the su(2)-spin system and its quantal fluctuations in the frame of the boson coherent state, the Holstein-Primakoff and Marumori-Yamamura-Tokunaga boson expansions are investigated. The starting point is found in the Schwinger boson representation for the su(2)-spin system and its reformation. Dirac's canonical theory for constraint systems is also applied to the su(2)-spin system. In conclusion, the latter boson expansion is found to be superior to the former with respect to the use of the boson coherent state.

Progress of Theoretical Physics•Jan 1, 1996•1 citation

A New Boson Realization of the Two-Level Pairing Model in a Many-Fermion System and Its Classical Counterpart: -- The Role of the su(2) su(1,1)-Coherent State in the Schwinger Boson Representation for the su(2) su(2)-Algebra --

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

A new method for describing the two-level pairing model in a many-fermion system is presented. The basic idea comes from the Schwinger boson representation for the su(2) ⊗ su(2)-algebra, in which four kinds of boson operators govern the dynamics. It is well known that in the original fermion space, it is almost impossible to introduce any trial state for the variation except the BCS state in the framework of the mean field approximation. However, in the Schwinger boson representation, various trial states can be defined on the condition that the mean field approximation is useful. In these states, the su(2) ⊗ su(1,1)-coherent state is mainly discussed in this paper.

Progress of Theoretical Physics•Apr 1, 2006•0 citations

A Possible Description of Many-Body System Composed of Three Kinds of Boson Operators: The su(2,1)-Boson Model

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

With the aim of investigating thermal effects in the su(2)-boson model recently proposed by the present authors, a possible su(2,1)-boson model is proposed. The basic idea comes from the use of three kinds of boson operators. Following the case of the su(1,1)-boson model, three aspects of the present model are investigated: mixed-mode coherent state, the classical counterpart, and its requantization.

Progress of Theoretical Physics•Nov 1, 1998•0 citations
In terms of the boson coherent state and a possible extension, three forms of wave packets are presented in the Schwinger boson representation. Each wave packet gives classical counterpart for a certain set of operators, for example, three components of the su(2)-spin. Furthermore, uncertainty relations which come from the boson coherent state and its extension are examined. The content discussed in this paper is, in a certain sense, an extension of that discussed in a paper presented recently by the present authors.
In the framework of the Marumori-Yamamura-Tokunaga boson expansion, three forms for the su(2)-spin system are presented. The first is related with the well-known Holstein-Primakoff boson expansion and the second is the expansion reinvestigated in a previous paper by the present authors. The third is, in some sense, the original part of this paper. Corresponding with three forms, c-number counterparts are obtained by using three forms of wave packets defined in the su(2)-spin space. With the help of appropriate quantization rule, they go back to the original boson expansions. Furthermore, it is discussed if the c-number counterparts can be regarded as the classical counterparts. Finally, the relation to the su(1, 1)-algebraic model is discussed.
With the aim of investigating dynamics of systems governed by su (1, 1)-algebra, a possible state which can give us a classical counterpart for the su (1, 1)-spin system properly is examined and constructed explicitly. By the use of canonicity conditions developed in the time-dependent Hartree-Fock theory, the c -number analogue of the Holstein-Primakoff boson representation is obtained for the su (1, 1)-algebra. It is noted that it is important to introduce a character of two-mode coherent state in order to present a suitable classical counterpart for the su (1, 1)-spin. Furthermore, it is shown that the spreading of uncertainty relations appears inevitably, which suggests that a certain fluctuation can be introduced.
With the aim of investigating dynamics of systems governed by su (1, 1)-algebra, a possible state which can give us a classical counterpart for the su (1, 1)-spin system properly is examined and constructed explicitly. By the use of canonicity conditions developed in the time-dependent Hartree-Fock theory, the c -number analogue of the Holstein-Primakoff boson representation is obtained for the su (1, 1)-algebra. It is noted that it is important to introduce a character of two-mode coherent state in order to present a suitable classical counterpart for the su (1, 1)-spin. Furthermore, it is shown that the spreading of uncertainty relations appears inevitably, which suggests that a certain fluctuation can be introduced.
With the aim of obtaining the classical counterpart of the su(2)-spin system and its quantal fluctuations in the frame of the boson coherent state, the Holstein-Primakoff and Marumori-Yamamura-Tokunaga boson expansions are investigated. The starting point is found in the Schwinger boson representation for the su(2)-spin system and its reformation. Dirac's canonical theory for constraint systems is also applied to the su(2)-spin system. In conclusion, the latter boson expansion is found to be superior to the former with respect to the use of the boson coherent state.
A new method for describing the two-level pairing model in a many-fermion system is presented. The basic idea comes from the Schwinger boson representation for the su(2) ⊗ su(2)-algebra, in which four kinds of boson operators govern the dynamics. It is well known that in the original fermion space, it is almost impossible to introduce any trial state for the variation except the BCS state in the framework of the mean field approximation. However, in the Schwinger boson representation, various trial states can be defined on the condition that the mean field approximation is useful. In these states, the su(2) ⊗ su(1,1)-coherent state is mainly discussed in this paper.