Dynamics of nuclear fluid. V. Extended time-dependent Hartree-Fock approximation illuminates the approach to thermal equilibrium

Journal Article · Mon Oct 01 00:00:00 EDT 1979 · Phys. Rev., C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.20.1419· OSTI ID:6032948

Wong, C; Tang, H H.K.

In the time-dependent Hartree-Fock approximation, the fermions are assumed to interact only through the mean field and the collisions between particles are neglected. We formulate an extended time-dependent Hartree-Fock approximation which incorporates particle collisions due to the residual interaction, with the usual time-dependent Hartree-Fock approximation as the collisionless limit. It is obtained by a truncation of the Martin-Schwinger hierarchy at the second level and by using a simple representation of the one-body Green's function in terms of time-dependent occupation numbers. The final set of coupled equations consists of a modified time-dependent Hartree-Fock equation and a master equation for the occupation numbers. These results are physically transparent and describe properly the physics of the collision process. They may also be simple enough to be of practical use to study heavy-ion collisions or the dynamics of other fermion systems. Furthermore, as the configuration-space analog of the quantum Boltzmann equation, many important results concerning statistical dynamics are obtained. Concepts such as entropy, temperature, and local and thermal equilibrium can be quantitatively introduced. The well-known H theorem that entropy never decreases can be readily recovered. With the collision term explicitly exhibited, the macroscopic equations (equations of continuity, momentum flux, and energy) and their associated conservation theorems can also be derived. Analytic solutions for the master equation for simple cases lead to new ''level crossing'' formulas having characteristics distinctly different from the Landau-Zener level-crossing formula and illuminate the salient features as to how a nonequilibrium fermion system approaches thermal equilibrium.

• Research Organization: Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830
• OSTI ID: 6032948
• Journal Information: Phys. Rev., C; (United States), Vol. 20:4
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
HARTREE-FOCK METHOD
TIME DEPENDENCE
NUCLEAR MATTER
THERMAL EQUILIBRIUM
BOLTZMANN EQUATION
ENTROPY
FERMIONS
FLUIDS
GREEN FUNCTION
H THEOREM
HEAVY ION REACTIONS
MANY-BODY PROBLEM
MARTIN-SCHWINGER THEORY
STATISTICAL MECHANICS
CHARGED-PARTICLE REACTIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUILIBRIUM
FUNCTIONS
MATTER
MECHANICS
NUCLEAR REACTIONS
PHYSICAL PROPERTIES
THERMODYNAMIC PROPERTIES
653003* - Nuclear Theory- Nuclear Reactions & Scattering
653002 - Nuclear Theory- Nuclear Matter
657006 - Theoretical Physics- Statistical Physics & Thermodynamics- (-1987)