Numerical study of chiral plasma instability within the classical statistical field theory approach

TL;DR

This study uses numerical simulations to explore the real-time dynamics of chiral plasma instability, revealing how fermionic backreaction influences chirality and electromagnetic field evolution, including inverse cascade phenomena.

Contribution

It provides the first detailed numerical analysis of chiral plasma instability using classical statistical field theory with lattice Dirac fermions and electromagnetic fields.

Findings

Fermionic backreaction prevents chirality imbalance accumulation.

Electric fields are screened during chirality pumping in parallel E and B fields.

Inverse cascade phenomena are observed, sometimes without axial charge decay.

Abstract

We report on a numerical study of real-time dynamics of electromagnetically interacting chirally imbalanced lattice Dirac fermions within the classical statistical field theory approach. Namely, we perform exact simulations of the real-time quantum evolution of fermionic fields coupled to classical electromagnetic fields, which are in turn coupled to the vacuum expectation value of the fermionic electric current. We use Wilson-Dirac Hamiltonian for fermions, and non-compact action for the gauge field. In general, we observe that the backreaction of fermions on the electromagnetic field prevents the system from acquiring chirality imbalance. In the case of chirality pumping in parallel electric and magnetic fields, electric field is screened by the produced on-shell fermions and the accumulation of chirality is hence stopped. In the case of evolution with initially present chirality imbalance, axial charge tends to transform to helicity of electromagnetic field. By performing simulations on large lattices we show that in most cases this decay process is accompanied by the inverse cascade phenomenon which transfers energy from short-wavelength to long-wavelength electromagnetic fields. In some simulations, however, we observe a very clear signature of inverse cascade for the helical magnetic fields which is not accompanied by the axial charge decay. This suggests that the relation between inverse cascade and axial charge decay is not as straightforward as predicted by the simplest form of anomalous Maxwell equations.