MagnetoHydrodynamics with chiral anomaly: phases of collective excitations and instabilities

TL;DR

This paper develops a relativistic chiral magnetohydrodynamics theory incorporating anomaly effects, revealing a phase transition between stable and unstable chiral fluids and identifying novel helical collective modes with instabilities.

Contribution

It formulates a low-energy effective CMHD theory including chiral anomaly effects and uncovers a phase transition and new collective modes with instabilities.

Findings

Identifies a phase transition at intermediate axial chemical potential.

Discovers four helical collective modes with two exhibiting exponential growth.

Maps the stability regime in a phase diagram based on chemical potential and wavevector angle.

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.