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.
Highlights
In recent years, there have been mounting interests in the transport of relativistic Weyl fermions in both nuclear physics and condensed matter systems
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
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 gradient and of the temperature and chemical-potential gradients
Summary
There have been mounting interests in the transport of relativistic Weyl fermions in both nuclear physics and condensed matter systems. Due to the involvement of side-jump terms in collisions, it is nontrivial to show the definition of local equilibrium distributions functions in a proper frame We tackle this issue first and focus on nonlinear responses with respect to local fluctuations away from equilibrium led by background fields and local temperature/ chemical-potential gradients for right-handed Weyl fermions. (2) Without applying anomalous hydrodynamic EOM, which corresponds to a system breaking energymomentum conservation due to the interaction with the environment, the quantum corrections of the second-order responses for charge currents under a “naive” RT approximation give the terms proportional to ∇ × E and E × ∇μ, which agree with the findings in [51,52].
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