Elements of Quantum Kinetic Theory

Charles D. Boley, Jeffrey B. Smith

Renormalized expressions for the transport coefficients of a normal quantum fluid are derived from a nonlocal kinetic equation. As was shown in the classical case by Forster and Martin and by R\'esibois, the expressions for the transport coefficients separate naturally into "kinetic" and "direct" parts. The kinetic terms are proportional to matrix elements of the inverse of the kinetic kernel, and have the same general structure as the "bare" transport coefficients obtained from a local Boltzmann equation. The direct terms are proportional to matrix elements of the kernel itself, and have no counterpart in calculations based on a local kinetic equation, as in the kinetic theory of gases. We evaluate the transport coefficients using the weak-coupling approximation to the kernel derived in a previous paper. Results are given, first, for both Bose and Fermi fluids at arbitrary temperature, and then for the Fermi fluid near $T=0$, where complete solutions are obtained. It is found that the direct parts of the shear viscosity and thermal conductivity are of higher order in $T$ than the kinetic parts, and are therefore negligible at very low temperature. The kinetic parts have the same leading temperature dependence as the predictions of the Landau theory. For the bulk viscosity, however, the direct and kinetic contributions begin at the same order (${T}^{2}$) in the temperature.

Fedir T. Vasko, O. É. Raichev

M. Bönitz

R. Walz, Kirill Boguslavski, Jürgen Berges

We consider an effective kinetic description for quantum many-body systems, which is not based on a weak-coupling or diluteness expansion. Instead, it employs an expansion in the number of field components $N$ of the underlying scalar quantum field theory. Extending previous studies, we demonstrate that the large-$N$ kinetic theory at next-to-leading order is able to describe important aspects of highly occupied systems, which are beyond standard perturbative kinetic approaches. We analyze the underlying quasiparticle dynamics by computing the effective scattering matrix elements analytically and solve numerically the large-$N$ kinetic equation for a highly occupied system far from equilibrium. This allows us to compute the universal scaling form of the distribution function at an infrared nonthermal fixed point within a kinetic description, and we compare to existing lattice field theory simulation results.

Mitsuo Shimoji

Daniel Charles Mattis

Elementary concepts in statistics and probability the Ising model and the lattice gas elements of thermodynamics statistical mechanics the world of bosons all about fermions kinetic theory the transfer matrix the uses of quantum field theory.