Effects of rotation and acceleration in the axial current: density operator vs Wigner function

TL;DR

This paper calculates third-order corrections to the axial current in quantum fluids, incorporating effects of rotation and acceleration, and compares two theoretical approaches for their consistency and differences.

Contribution

It introduces a detailed third-order perturbative calculation of the axial current including acceleration effects and compares the density operator and Wigner function methods.

Findings

Both methods agree when acceleration is zero.

Differences arise when both acceleration and vorticity are significant.

The results extend understanding of chiral effects in rotating quantum systems.

Abstract

The hydrodynamic coefficients in the axial current are calculated on the basis of the equilibrium quantum statistical density operator in the third order of perturbation theory in thermal vorticity tensor both for the case of massive and massless fermions. The coefficients obtained describe third-order corrections to the Chiral Vortical Effect and include the contribution from local acceleration. We show that the methods of the Wigner function and the statistical density operator lead to the same result for an axial current in describing effects associated only with vorticity when the local acceleration is zero, but differ in describing mixed effects for which both acceleration and vorticity are significant simultaneously.