Particle Production and Effective Thermalization in Inhomogeneous Mean Field Theory

TL;DR

This study uses a 1+1 dimensional abelian Higgs model with fermions to explore particle production and local thermalization in a nonequilibrium quantum field theory setting, employing numerical solutions of inhomogeneous mean field equations.

Contribution

It introduces a numerical approach to analyze particle production and thermalization in an inhomogeneous quantum field model with coupled gauge and fermion fields.

Findings

Fermions approximately thermalize locally in time.

Particle production can be characterized by a time-dependent temperature and chemical potential.

Inhomogeneous gauge fields induce Coulomb scattering effects.

Abstract

As a toy model for dynamics in nonequilibrium quantum field theory we consider the abelian Higgs model in 1+1 dimensions with fermions. In the approximate dynamical equations, inhomogeneous classical (mean) Bose fields are coupled to quantized fermion fields, which are treated with a mode function expansion. The effective equations of motion imply e.g. Coulomb scattering, due to the inhomogeneous gauge field. The equations are solved numerically. We define time dependent fermion particle numbers with the help of the single-time Wigner function and study particle production starting from inhomogeneous initial conditions. The particle numbers are compared with the Fermi-Dirac distribution parametrized by a time dependent temperature and chemical potential. We find that the fermions approximately thermalize locally in time.