Nonlinear Responses of Chiral Fluids from Kinetic Theory

TL;DR

This paper investigates the second-order nonlinear responses of inviscid chiral fluids using kinetic theory, revealing quantum corrections' effects on anomalous transport phenomena and charge density behavior.

Contribution

It introduces a novel approach to analyze nonlinear responses in chiral fluids considering quantum corrections within kinetic theory and the relaxation-time approximation.

Findings

Quantum corrections lead to anomalous charge Hall currents.

Nonlinear quantum corrections to charge density vanish under classical RT approximation.

Local equilibrium distribution can be non-trivially defined in a co-moving frame.

Abstract

The second-order nonlinear responses of inviscid chiral fluids near local equilibrium are investigated by applying the chiral kinetic theory (CKT) incorporating side-jump effects. It is shown that the local equilibrium distribution function can be non-trivially introduced in a co-moving frame with respect to the fluid velocity when the quantum corrections in collisions are involved. For the study of anomalous transport, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (RT) approximation, which result in anomalous charge Hall currents propagating along the cross product of the background electric field and the temperature (or chemical-potential) gradient and of the temperature and chemical-potential gradients. On the other hand, the nonlinear quantum correction on the charge density vanishes in the classical RT approximation, which in fact satisfies the matching condition given by the anomalous equation obtained from the CKT.