Anomalous Hall instability in the Chern-Simons magnetohydrodynamics

Abstract

The Chern-Simons magnetohydrodynamics (CSMHD) is introduced using a Maxwell-Chern-Simons (MCS) Lagrangian including an axion-like field $\Theta$. The MCS equation of motion derived from this Lagrangian consists of a modified current, including a chiral magnetic (CM) and an anomalous Hall (AH) current, in addition to the ordinary Ohm current of resistive magnetohydrodynamics (MHD). The former consists of an axial chemical potential, which is given in terms of the temporal comoving derivative of $\Theta$, and the latter arises from the spatial gradient of $\Theta$. As it turns out, the existence of the axial chemical potential is a nonequilibrium effect that plays no role in the linear stability analysis, whereas the AH current arises as in the first-order linear perturbation of the thermal equilibrium. We analyze the linear stability and causality of the CSMHD in a resistive and chiral medium. We show that the Alfven modes propagating sufficiently close to the direction of the magnetic field are unstable but causal. They are also accompanied by a genuine nonhydro mode. A stable mode in a particular direction can correspond to an unstable mode propagating in the exact opposite direction. The AH instability is a manifestation of a breakdown of the parity. A numerical analysis of the phase velocity confirms these results.

arXiv comment31 pages, 10 figures

References in corpus (33)

• The Chiral Magnetic Effect
• The effects of topological charge change in heavy ion collisions: "Event by event P and CP violation"
• Hydrodynamics with Triangle Anomalies
• Elliptic and triangular flow in event-by-event (3+1)D viscous hydrodynamics
• 3+1D hydrodynamic simulation of relativistic heavy-ion collisions
• Lectures on hydrodynamic fluctuations in relativistic theories
• The production of photons in relativistic heavy-ion collisions
• New theories of relativistic hydrodynamics in the LHC era
• Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
• Electromagnetic fields and anomalous transports in heavy-ion collisions --- A pedagogical review
• First-order relativistic hydrodynamics is stable
• Notes on Anomaly Induced Transport
• Relativistic fluid dynamics with spin
• Topologically induced local P and CP violation in QCD x QED
• Does stability of relativistic dissipative fluid dynamics imply causality?
• Relativistic magnetohydrodynamics
• Covariant statistical mechanics and the stress-energy tensor
• Do nuclear collisions create a locally equilibrated quark-gluon plasma?
• Anomaly inflow and thermal equilibrium
• Resistive dissipative magnetohydrodynamics from the Boltzmann-Vlasov equation
• Magnetohydrodynamics of Chiral Relativistic Fluids
• Anomalous Hydrodynamics
• Laminar and turbulent dynamos in chiral magnetohydrodynamics-I: Theory
• MagnetoHydrodynamics with chiral anomaly: phases of collective excitations and instabilities
• Thermodynamics of polarized relativistic matter
• Hydrodynamical instabilities in an expanding quark gluon plasma
• Novel self-similar rotating solutions of non-ideal transverse magnetohydrodynamics
• Maxwell-Chern-Simons Hydrodynamics for the Chiral Magnetic Effect
• The overdamped chiral magnetic wave
• Modification of magnetohydrodynamic waves by the relativistic Hall effect
• Perfect magnetohydrodynamics as a field theory
• The effect of magnetization and electric polarization on the anomalous transport coefficients of a chiral fluid
• Rotating solutions of nonideal transverse Chern-Simons magnetohydrodynamics and the anomalous Hall current

Cited by in corpus (2)

• Can we make sense of dissipation without causality?
• Thermodynamic stability implies causality