Kinetic equation for strongly interacting dense Fermi systems

Abstract

We review the non-relativistic Green's-function approach to the kinetic equations for Fermi liquids far from equilibrium. The emphasis is on the consistent treatment of the off-shell motion between collisions and on the non-instant and non-local picture of binary collisions. The resulting kinetic equation is of the Boltzmann type, and it represents an interpolation between the theory of transport in metals and the theory of moderately dense gases. The free motion of particles is renormalised by various mean field and mass corrections in the spirit of Landau's quasiparticles in metals. The collisions are non-local in the spirit of Enskog's theory of non-ideal gases. The collisions are moreover non-instant, a feature which is absent in the theory of gases, but which is shown to be important for dense Fermi systems. In spite of its formal complexity, the presented theory has a simple implementation within the Monte-Carlo simulation schemes. Applications in nuclear physics are given for heavy-ion reactions and the results are compared with the former theory and recent experimental data. The effect of the off-shell motion and the non-local and non-instant collisions on the dynamics of the system can be characterised in terms of thermodynamic functions such as the energy density or the pressure tensor. Non-equilibrium counterparts of these functions and the corresponding balance equations are derived and discussed from two points of view. Firstly, they are used to prove the conservation laws. Secondly, the role of individual microscopic mechanisms in fluxes of particles and momenta and in transformations of the energy is clarified.Comment: Boo

A continuum model of gas flows with localized density variations

“…A correction of this asymmetry can be based on the concept of non-local and non-instant collisions [3]. However, this asymmetry may also be corrected by supplementing the Boltzmann description with a proper description of spatial variations of the molecules.…”

“…The Boltzmann kinetic equation has received a number of derivations under specific assumptions which all aim to prove its physical and mathematical rigour [2]. It is also widely accepted that continuum fluid mechanical models, and associated classical thermodynamic models, in particular equations of state, can be obtained from the statistical kinetic formulations [3]. For example, it is well-known that the three classical fluid dynamic equations, the Navier-Stokes equations, may be derived from the Boltzmann kinetic equation [4].…”

Range of validity of transport equations

“…However, if they are not applied then a gradient expansion would become too cumbersome to be of use in practical calculations. The derivation of transport equations has been discussed in great detail in the literature [14,15,16,17,18,19,20,21,22,23,24,25,26]. Most discussions focus on kinetic theory employing the additional approximation of a suitable quasi-particle ansatz, which goes beyond assumptions 1) -3).…”

Midrapidity charge distribution in peripheral heavy ion collisions

“…Although their discussion is limited to the equilibrium, it marks a way how to introduce virial corrections also to dynamical processes. The kinetic equation for quasiparticles with non-instantaneous and non-local scattering integral has been derived in [37,54] as a systematic quasi-classical limit of non-equilibrium Green's functions in the Galitskii-Feynman approximation. It has been shown that the gradient corrections to the scattering integral can be rearranged into a form of a collision delay and space displacements reminiscent of classical hard spheres, i.e., into a form suitable for numerical simulations.…”

“…In this contribution we will put these ideas of nonlocalities on the firm ground using the quantum kinetic equation with nonlocal scattering integrals which was derived from quantum statistics [37,54] to show how the effect of nonlocalities play a role in simulations of heavy ion reactions and compare them with experiment.…”