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

Journal Article · Sat Mar 01 04:00:00 EST 1980 · Phys. Rev., C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.21.1098· OSTI ID:5482512

Kan, K; Lichtner, P C; Dworzecka, M; Griffin, J J

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 two-body 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.

• Research Organization: Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742
• OSTI ID: 5482512
• Journal Information: Phys. Rev., C; (United States), Journal Name: Phys. Rev., C; (United States) Vol. 21:3; ISSN PRVCA
• Country of Publication: United States
• Language: English

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73 NUCLEAR PHYSICS AND RADIATION PHYSICS
CLASSICAL MECHANICS
FUNCTIONS
HAMILTONIANS
HARTREE-FOCK METHOD
MANY-BODY PROBLEM
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MECHANICS
NUCLEAR STRUCTURE
PHASE SPACE
QUANTUM OPERATORS
SPACE
TIME DEPENDENCE
VARIATIONAL METHODS
WAVE FUNCTIONS