A kinetic equation for spin polarized Fermi systems

TL;DR

This paper develops a kinetic Boltzmann equation for spin-polarized Fermi gases with matrix-valued distribution functions, proving global existence of solutions in a periodic domain.

Contribution

It introduces a new kinetic equation with a general collision kernel for spin-dependent Fermi gases and establishes the global existence of weak solutions.

Findings

Proves global existence of bounded weak solutions in L1 space.

Models spin-dependent Fermi gases with matrix-valued distribution functions.

Handles a general type of collision kernel.

Abstract

This paper a kinetic Boltzmann equation having a general type of collision kernel and modelling spin-dependent Fermi gases at low temperatures modelled by a kinetic equation of Boltzmann type. The distribution functions have values in the space of positive hermitean 2x2 complex matrices. Global existence of bounded weak solutions is proved in L1 to the initial value problem in a periodic box.