Parity violating quantum kinetic theory in (2+1)-dimensions

TL;DR

This paper develops a kinetic theory framework for (2+1)-dimensional fermionic systems, revealing parity-violating transport phenomena like Hall conductivity and vorticity effects without considering collisions.

Contribution

It introduces a Wigner function approach to derive hydrodynamical transport coefficients in (2+1)D, including novel vorticity-dependent effects, neglecting fermion collisions for a dissipationless model.

Findings

Parity violating Hall conductivity matches quantum field theory results.

Vorticity-dependent transport properties naturally emerge.

The model is dissipationless due to neglecting collisions.

Abstract

We study the kinetic theory for a (2+1)-dimensional fermionic system with special emphasis on the parity violating properties associated with the fermion mass. The Wigner function approach is used to derive hydrodynamical transport coefficients to the first spatial derivative order. As a first attempt, the collisions between fermions are neglected. The resulting system is dissipationless. The parity violating Hall electric conductivity has the same temperature and chemical potential dependence as the quantum field theory result at one-loop. Vorticity dependent transport properties, which were not considered before, also emerge naturally in this approach.