Chiral Magnetic Effect out of equilibrium

TL;DR

This paper investigates the behavior of the chiral magnetic conductivity in out-of-equilibrium relativistic fermionic systems, revealing its dependence on frequency and the non-regularity of the zero-frequency limit.

Contribution

It provides a calculation of the frequency-dependent chiral magnetic conductivity in lattice models with time-dependent chiral chemical potential, highlighting the non-regularity of the zero-frequency limit.

Findings

$\sigma_{CME}(\omega)$ approaches the conventional value 1 at nonzero frequencies in the continuum limit.

$\sigma_{CME}$ is zero when the chiral chemical potential is time-independent.

The zero-frequency limit is non-regular for infinite massless fermion systems.

Abstract

We consider relativistic fermionic systems in lattice regularization out of equilibrium. The chiral magnetic conductivity $\sigma_{CME}$ is calculated in spatially infinite system for the case when the chiral chemical potential depends on time while the system initially was in thermal equilibrium at small but nonzero temperature. We find that the frequency dependent $\sigma_{CME}(\omega)$ for any nonzero $\omega$ both in the limits $\omega \ll T$ and $\omega \gg T$ is equal to its conventional value $1$ when the lattice model approaches continuum limit. Notice that $\sigma_{CME} = 0$ for the case when the chiral chemical potential does not depend on time at all. We therefore confirm that the limit of vanishing $\omega$ is not regular for the spatially infinite systems of massless fermions.