On the quantum Boltzmann equation

TL;DR

This paper presents a nonrigorous derivation of the nonlinear quantum Boltzmann equation from the Schrödinger evolution of interacting fermions, relying on the concept of restricted quasifreeness in the weak coupling limit.

Contribution

It introduces the notion of restricted quasifreeness and uses it to connect Schrödinger dynamics with the quantum Boltzmann equation.

Findings

Derivation based on quasifree initial states

Assumption of restricted quasifreeness in weak coupling limit

Provides a framework for understanding fermionic quantum kinetics

Abstract

We give a nonrigorous derivation of the nonlinear Boltzmann equation from the Schrodinger evolution of interacting fermions. The argument is based mainly on the assumption that a quasifree initial state satisfies a property called restricted quasifreeness in the weak coupling limit at any later time. By definition, a state is called restricted quasifree if the four-point and the eight-point functions of the state factorize in the same manner as in a quasifree state.