Magnetohydrodynamics with chiral anomaly: Phases of collective excitations and instabilities

Koichi Hattori,Ho-Ung Yee,Yuji Hirono,Yi Yin

doi:10.1103/physrevd.100.065023

Abstract

We study the relativistic hydrodynamics with chiral anomaly and dynamical electromagnetic fields, namely Chiral MagnetoHydroDynamics (CMHD). We formulate CMHD as a low-energy effective theory based on a generalized derivative expansion. We demonstrate that the modification of ordinary MagnetoHydroDynamics (MHD) due to chiral anomaly can be obtained from the second law of thermodynamics and is tied to chiral magnetic effect. We further study the real-time properties of chiral fluid by solving linearized CMHD equations. We discover a remarkable "transition" at an intermediate axial chemical potential $\mu_{A}$ between a stable Chiral fluid at low $\mu_{A}$ and an unstable Chiral fluid at large $\mu_{A}$. We summarize this transition in a "phase diagram" in terms of $\mu_{A}$ and the angle of the wavevector relative to the magnetic field. In the unstable regime, there are four collective modes carrying both magnetic and fluid helicity, in contrary to MHD waves which are unpolarized. The half of the helical modes grow exponentially in time, indicating the instability, while the other half become dissipative.

Highlights

Hydrodynamics is a versatile theory describing the realtime dynamics of a given interacting many-body system in the long-time limit [1]
We wish to present a hydrodynamic approach for conducting chiral fluid by coupling the dynamics of axial charge density nA to MHD, and we refer to the resulting theory as chiral MHD
We have presented a formulation of hydrodynamic theory for a chiral fluid with a dynamical magnetic field based on a generalization of derivative expansion

Summary

INTRODUCTION

Hydrodynamics is a versatile theory describing the realtime dynamics of a given interacting many-body system in the long-time limit [1]. The dynamical variables of MHD include ε and uμ, but the magnetic field Bμ as well. We wish to present a hydrodynamic approach for conducting chiral fluid by coupling the dynamics of axial (chiral) charge density nA to MHD, and we refer to the resulting theory as chiral MHD (CMHD); see Refs. [15] for a discussion on the extension of hydrodynamics with parametrically slow modes in generic situations) We identify this additional small parameter as the anomaly coefficient CA [see Eq (3) below], and we will work in the limit CA ≪ 1. The formulation of CMHD based on a new derivative expansion scheme together with the discovery of a qualitative difference in the dynamical properties of chiral fluid are the main findings of this paper

CHIRAL MHD

COLLECTIVE MODES

SUMMARY AND IMPLICATIONS

The constitutive relation at zeroth order in δ

The constitutive relation at first order in chiral MHD and CME