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

arXiv:nucl-th/0610073 · Progress of Theoretical Physics

Semi-Classical Approach to the Two-Level Pairing Model: Various Aspects of Phase Change

Y. Tsue, C. Providencia, João da Providência, M. Yamamura

Published Mar 1, 2007• 1 citation
arXivHTMLPDF

Abstract

Properties of the phase change of the two-level pairing model are investigated in the semi-classical treatment by using the variational approach with a mixed-mode coherent state. In the classical limit, ħ → 0, a sharp phase transition appears, and the two phases exist in the region where the force strength is larger than a certain critical value. However, it is shown that, in the semi-classical treatment, the above-mentioned behavior of the phase change disappears in both analytical and numerical treatments. This leads to a new understanding of the properties of the phase change in this model.

DOI
10.1143/ptp.117.431

Related papers

Semi-Classical Approach to the Two-Level Pairing Model Various Aspects of Phase Change

Yasuhiko Tsue, Constança Providência

Aspects of the phase change of the two-level pairing model are investigated in the semi-classical treatment by using the variational approch with the mixed-mode coherent state. In the classical limit, � → 0, the sharp phase transition appears and the two phases exist in the region where the force strength is larger than a certain critical value. However, it is shown that, in the semi-classical treatment, the abovementioned behavior of the phase change disappears in the analytical and the numerical treatments. As a result, new understanding about aspects of the phase change in this model is given. The phase structure and the phase transitions between various phases in condensed matter systems, such as nuclear and/or quark matter as well as the condensed matter in atoms and molecules, are important concepts to understand the nature of the matter under consideration. In the infinite systems, the clear phase separation is often realized and, in that

•Jan 1, 2006•1 citation

Phase transition in the pairing-plus-quadrupole model

C. Bahri, DAVID J. ROWE, Wasantha Wijesundera

We consider the pairing-plus-quadrupole model Hamiltonian within the framework of a many-fermion shell model. The Hamiltonian exhibits a transition from a superconducting to a rotational phase with variation of a parameter. The model has analytical solutions in its two limits due to the presence of dynamical symmetries. However, the symmetries are basically incompatible with one another which means that no simple solution exists in intermediate situations. Exact (numerical) solutions are nevertheless possible on a computer and enable one to study the behavior of competing but incompatible symmetries and the phase transitions that result in a semirealistic situation. This mixed-symmetry dynamics generates a rich structure which gives new insight for the study of phase transitions.

Physical Review C•Sep 1, 1998•45 citations

Classical and Quantal Descriptions of Small Amplitude Fluctuations around Equilibriums in the Two-Level Pairing Model

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

Various classical counterparts to the two-level pairing model in a many-fermion system are presented in the Schwinger boson representation. It is shown that one of the key ingredients giving the classical descriptions for quantal systems is the use of various trial states in addition to the su(2) ⊗ su(2)-coherent state, which may be a natural selection for the two-level pairing model governed by the su(2) ⊗ su(2)-algebra. It is pointed out that a spurious behavior such as a sharp phase transition can be avoided by using the other states including the su(2) ⊗ su(1,1)- and su(1,1) ⊗ su(1,1)-coherent states. This contrasts with the situation regarding the usual Hartree-Fock-Bogoliubov and quasi-particle random phase approximations applied to the original fermion system, which yield a sharp phase transition.

arXiv:nucl-th/0610074•Progress of Theoretical Physics•May 1, 2007•0 citations

A New Boson Realization of Two-Level Pairing Model in Many-Fermion System and its Classical Counterpart

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. Basic idea comes from the Schwinger boson representation for the su(2) cross 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 mixed-mode coherent state is mainly discussed in this paper.

arXiv:nucl-th/0601087•Jan 30, 2006•0 citations

A Refined Numerical Result on the First Excitation Energy in the Two-Level Pairing Model

Y. Tsue, C. Providencia, João da Providência +1 more

The first excitation energy in the two-level pairing model is investigated in terms of the equilibrium and the small fluctuation around it. The basic idea is an extension of results presented in a previous paper by the present authors. In this investigation, the result obtained in the previous paper plays a central role: At the limit of the weak and the strong interaction strength, the results are in good agreement with the exact one. The former and the latter are calculated in the framework of the $su(2)\otimes su(1,1)$- and the $su(2)\otimes su(2)$-coherent state, respectively. On the basis of the above conclusion, the intermediate region for the interaction strength is described in terms of the idea of the interpolation and it is shown that the agreement of the result with the exact one is quite good.

arXiv:nucl-th/0701019•Progress of Theoretical Physics•May 1, 2007•0 citations

Enhancing quantum phase transitions in the critical point of Extended TC-Dicke model via Stark effect

Ahmed Salah, A. S. Abdel-Rady, Abdel-Nasser A. Osman +1 more

A system of N two-level atoms, Tavis-Cummings Dicke (TC-Dicke) model, interacting with a one-mode electromagnetic radiation field in the presence of the Stark shifts is studied, which is expected to predict new phenomena that are not explored in the original TC-Dicke model. We obtained the potential energy surface of the system using a trial state the direct product of coherent states in each subspace. In the frame of mean-field approaches, the variational energy is evaluated as the expectation value of the Hamiltonian for this state. The order of the quantum phase transitions is determined explicitly and numerically. We estimate the ground-state energy and the macroscopic excitations in the superradiant phase. Moreover, we investigated the critical properties of the TC-Dicke model in the classical spin limit and coherent state. We observed that in the thermodynamic limit, the energy surface takes a simple form a direct description of the phase transition. Moreover, it is found that when the microwave amplitude changes the new phase transition occurs with the Stark shift. The analytical solutions and numerical results, which appear in this paper are agreement with our paper which published recently in Int. J. Mod. Phys. B when we studied the same model using a different coherent state.

Scientific Reports•Jul 27, 2018•13 citations
Properties of the phase change of the two-level pairing model are investigated in the semi-classical treatment by using the variational approach with a mixed-mode coherent state. In the classical limit, ħ → 0, a sharp phase transition appears, and the two phases exist in the region where the force strength is larger than a certain critical value. However, it is shown that, in the semi-classical treatment, the above-mentioned behavior of the phase change disappears in both analytical and numerical treatments. This leads to a new understanding of the properties of the phase change in this model.
Aspects of the phase change of the two-level pairing model are investigated in the semi-classical treatment by using the variational approch with the mixed-mode coherent state. In the classical limit, � → 0, the sharp phase transition appears and the two phases exist in the region where the force strength is larger than a certain critical value. However, it is shown that, in the semi-classical treatment, the abovementioned behavior of the phase change disappears in the analytical and the numerical treatments. As a result, new understanding about aspects of the phase change in this model is given. The phase structure and the phase transitions between various phases in condensed matter systems, such as nuclear and/or quark matter as well as the condensed matter in atoms and molecules, are important concepts to understand the nature of the matter under consideration. In the infinite systems, the clear phase separation is often realized and, in that
We consider the pairing-plus-quadrupole model Hamiltonian within the framework of a many-fermion shell model. The Hamiltonian exhibits a transition from a superconducting to a rotational phase with variation of a parameter. The model has analytical solutions in its two limits due to the presence of dynamical symmetries. However, the symmetries are basically incompatible with one another which means that no simple solution exists in intermediate situations. Exact (numerical) solutions are nevertheless possible on a computer and enable one to study the behavior of competing but incompatible symmetries and the phase transitions that result in a semirealistic situation. This mixed-symmetry dynamics generates a rich structure which gives new insight for the study of phase transitions.
Various classical counterparts to the two-level pairing model in a many-fermion system are presented in the Schwinger boson representation. It is shown that one of the key ingredients giving the classical descriptions for quantal systems is the use of various trial states in addition to the su(2) ⊗ su(2)-coherent state, which may be a natural selection for the two-level pairing model governed by the su(2) ⊗ su(2)-algebra. It is pointed out that a spurious behavior such as a sharp phase transition can be avoided by using the other states including the su(2) ⊗ su(1,1)- and su(1,1) ⊗ su(1,1)-coherent states. This contrasts with the situation regarding the usual Hartree-Fock-Bogoliubov and quasi-particle random phase approximations applied to the original fermion system, which yield a sharp phase transition.
A new method for describing the two-level pairing model in a many-fermion system is presented. Basic idea comes from the Schwinger boson representation for the su(2) cross 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 mixed-mode coherent state is mainly discussed in this paper.
The first excitation energy in the two-level pairing model is investigated in terms of the equilibrium and the small fluctuation around it. The basic idea is an extension of results presented in a previous paper by the present authors. In this investigation, the result obtained in the previous paper plays a central role: At the limit of the weak and the strong interaction strength, the results are in good agreement with the exact one. The former and the latter are calculated in the framework of the su(2)⊗su(1,1)su(2)\otimes su(1,1)su(2)⊗su(1,1)- and the su(2)⊗su(2)su(2)\otimes su(2)su(2)⊗su(2)-coherent state, respectively. On the basis of the above conclusion, the intermediate region for the interaction strength is described in terms of the idea of the interpolation and it is shown that the agreement of the result with the exact one is quite good.
A system of N two-level atoms, Tavis-Cummings Dicke (TC-Dicke) model, interacting with a one-mode electromagnetic radiation field in the presence of the Stark shifts is studied, which is expected to predict new phenomena that are not explored in the original TC-Dicke model. We obtained the potential energy surface of the system using a trial state the direct product of coherent states in each subspace. In the frame of mean-field approaches, the variational energy is evaluated as the expectation value of the Hamiltonian for this state. The order of the quantum phase transitions is determined explicitly and numerically. We estimate the ground-state energy and the macroscopic excitations in the superradiant phase. Moreover, we investigated the critical properties of the TC-Dicke model in the classical spin limit and coherent state. We observed that in the thermodynamic limit, the energy surface takes a simple form a direct description of the phase transition. Moreover, it is found that when the microwave amplitude changes the new phase transition occurs with the Stark shift. The analytical solutions and numerical results, which appear in this paper are agreement with our paper which published recently in Int. J. Mod. Phys. B when we studied the same model using a different coherent state.