Geometrized dynamics and search of structural instabilities in SU(2) models

Journal Article · Wed Apr 01 04:00:00 EST 1987 · Phys. Rev. C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.35.1555· OSTI ID:6728817

Jezek, D M; Hernandez, E S

The structural instabilities or general nonthermodynamic phase transitions of the time-dependent Hartree-Fock flow on the Bloch sphere are investigated for different SU(2) model Hamiltonians by means of a simple geometrical construction. In particular, the generalized Lipkin-Meshkov-Glick model is found to exhibit a variety of instabilities, opposite to the standard Lipkin-Meshkov-Glick model which possesses only one ground-state (thermodynamic) phase transition. The relationship between the fixed points of the time-dependent Hartree-Fock flow and the tangency points between energy surfaces and the Bloch sphere is established. It is found that different Hamiltonians of the class under study give rise to flow patterns whose invariant sets may contain either rotations or librations, which in turn may be degenerate as well as nondegenerate, in contrast to previously investigated models.

• Research Organization: Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
• OSTI ID: 6728817
• Journal Information: Phys. Rev. C; (United States), Journal Name: Phys. Rev. C; (United States) Vol. 35:4; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

653001* -- Nuclear Theory-- Nuclear Structure
Moments
Spin
& Models
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
HAMILTONIANS
HARTREE-FOCK METHOD
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
P INVARIANCE
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
PHASE SPACE
PHASE TRANSFORMATIONS
QUANTUM OPERATORS
SPACE
STATISTICAL MODELS
SU GROUPS
SU-2 GROUPS
SYMMETRY BREAKING
SYMMETRY GROUPS
THERMODYNAMIC MODEL
TIME DEPENDENCE