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

Journal of Physics A Mathematical and General

Correlations studies in the q-deformed time-dependent Hartree-Fock approximation

Sidney S. Avancini, F. Cruz, Débora Peres Menezes, Mello Moraes

Published Feb 7, 1995• 2 citations
Publisher

Abstract

In this work we investigate the differences arising in the one-body operator and the correlation parameter when the Lipkin-Meshkov-Glick model is deformed. We calculate these functions exactly and by means of the time-dependent Hartree-Fock approximation (TDHF). We observe that the exact and the TDHF results are much closer to each other in the deformed case.

DOI
10.1088/0305-4470/28/3/023

Related papers

THE UNDERLYING PHYSICS OF q-DEFORMED PSEUDOSPIN MODELS

Sidney S. Avancini, Débora Peres Menezes, F. Cruz +1 more

In this paper, we have used the q-deformed version of the Lipkin-Meshkov-Glick (LMG) model to summarize the utilization of quantum algebras already applied to soluble pseudospin models. Within the suq(2) context, we have checked the validity of the co herent states variational method, then used the Time Dependent Hartree-Fock (TDHF) approximation to compare with the exact evolution in time of the system, and finally observed the temperature effects undergone by the system, through the study of the Helmholtz free energy. We have also investigated the LMG model within the contexts of the supq(2) and suq(3) algebras and some of the features mentioned above have been rediscussed.

International Journal of Modern Physics E•Jun 1, 1996•1 citation

Time-dependent Hartree-Fock dynamics and phase transition in Lipkin-Meshkov-Glick model

Kit-Keung Kan, Peter C. Lichtner, Maria Dworzecka +1 more

The time-dependent Hartree-Fock solutions of the two-level Lipkin-Meshkov-Glick model are studied by transforming the time-dependent Hartree-Fock equations into Hamilton's canonical form and analyzing the qualitative structure of the Hartree-Fock energy surface in the phase space. It is shown that as the interaction strength increases these time-dependent Hartree-Fock solutions undergo a qualitative change associated with the ground state phase transition previously studied in terms of coherent states. For twobody interactions stronger than the critical value, two types of time-dependent Hartree-Fock solutions (the "librations" and "rotations" in Hamilton's mechanics) exist simultaneously, while for weaker interactions only the rotations persist. It is also shown that the coherent states with the maximum total pseudospin value are determinants, so that time-dependent Hartree-Fock analysis is equivalent to the coherent state method.NUCLEAR STRUCTURE Lipkin-Meshkov-Glick model, TDHF, transformation of TDHF equations to Hamilton's canonical form, coherent states, ground state phase transition.

Physical Review C•Mar 1, 1980•42 citations

Dynamics of the q-deformed Lipkin model

Sidney S. Avancini, Débora Peres Menezes, Mello Moraes +1 more

In this paper we investigate the dynamics of the Lipkin-Meshkov-Glick model within the context of quantum algebras. For this purpose we obtain the equations of motion with the help of the time-dependent variational principle. To analyse the results, graphs for equi-energies, potentials and mean-square deviation of the J z operator have been plotted. Modifications in the usual libration and rotational motions due to the introduction of quantum deformation are discussed.

Journal of Physics A Mathematical and General•Feb 7, 1994•8 citations

Investigation of Ground-State Correlations for a Model Hamiltonian of the Nucleus

Jitendra C. Parikh, DAVID J. ROWE

The importance of ground-state correlations in the spectroscopy of a finite many-particle system, such as the nucleus, is investigated for the model Hamiltonian of Lipkin, Meshkov, and Glick. In particular, we have investigated their effect on the solution of the equations of motion for excitation energies, transition matrix elements, and the correlation energy of the ground state. Methods are studied for calculating the correlations needed to make the necessary corrections to the equations of motion. Also studied is the behavior, with increase of interaction strength, of the phase transition from the spherical to the strongly deformed intrinsic states, in the projected Hartree-Fock scheme.

Physical Review•Nov 20, 1968•65 citations

Theories for multiple resonances

Dietrich Klakow, M. Weber, P.‐G. Reinhard

Two microscopic theories for multiple resonances in nuclei are compared, n-particle-hole RPA and quantized Time-Dependent Hartree-Fock (TDHF). The Lipkin-Meshkov-Glick model is used as test case. We find that quantized TDHF is superior in many respects, except for very small systems. 1

•Jan 1, 1995•4 citations

OCCUPATION RENORMALIZED HARTREE-FOCK APPROXIMATION IN LIPKIN MODEL

Pan Zhang

The occupation renormalized Hartree-Fock single particle potential is extended to include the 'particle' state occupation. The exact solution, the solution of the occupation renormalized Hartree-Fock approximation and that of the Hartree-Fock approximation are calculated in Lipkin Model. It turns out that the RHF solution is more close to the exact one than the HF solution. The effect of occupation probability depends on the strength of the interaction of the two body term.

Chinese Physics C•Jan 1, 1984•0 citations
In this work we investigate the differences arising in the one-body operator and the correlation parameter when the Lipkin-Meshkov-Glick model is deformed. We calculate these functions exactly and by means of the time-dependent Hartree-Fock approximation (TDHF). We observe that the exact and the TDHF results are much closer to each other in the deformed case.
In this paper, we have used the q-deformed version of the Lipkin-Meshkov-Glick (LMG) model to summarize the utilization of quantum algebras already applied to soluble pseudospin models. Within the suq(2) context, we have checked the validity of the co herent states variational method, then used the Time Dependent Hartree-Fock (TDHF) approximation to compare with the exact evolution in time of the system, and finally observed the temperature effects undergone by the system, through the study of the Helmholtz free energy. We have also investigated the LMG model within the contexts of the supq(2) and suq(3) algebras and some of the features mentioned above have been rediscussed.
The time-dependent Hartree-Fock solutions of the two-level Lipkin-Meshkov-Glick model are studied by transforming the time-dependent Hartree-Fock equations into Hamilton's canonical form and analyzing the qualitative structure of the Hartree-Fock energy surface in the phase space. It is shown that as the interaction strength increases these time-dependent Hartree-Fock solutions undergo a qualitative change associated with the ground state phase transition previously studied in terms of coherent states. For twobody interactions stronger than the critical value, two types of time-dependent Hartree-Fock solutions (the "librations" and "rotations" in Hamilton's mechanics) exist simultaneously, while for weaker interactions only the rotations persist. It is also shown that the coherent states with the maximum total pseudospin value are determinants, so that time-dependent Hartree-Fock analysis is equivalent to the coherent state method.NUCLEAR STRUCTURE Lipkin-Meshkov-Glick model, TDHF, transformation of TDHF equations to Hamilton's canonical form, coherent states, ground state phase transition.
The importance of ground-state correlations in the spectroscopy of a finite many-particle system, such as the nucleus, is investigated for the model Hamiltonian of Lipkin, Meshkov, and Glick. In particular, we have investigated their effect on the solution of the equations of motion for excitation energies, transition matrix elements, and the correlation energy of the ground state. Methods are studied for calculating the correlations needed to make the necessary corrections to the equations of motion. Also studied is the behavior, with increase of interaction strength, of the phase transition from the spherical to the strongly deformed intrinsic states, in the projected Hartree-Fock scheme.