Non-Gaussian diffusive fluctuations in Dirac fluids

TL;DR

This paper predicts that charge transport in Dirac fluids exhibits highly non-Gaussian fluctuations, with a specific asymptotic form of full counting statistics, leading to enhanced charge noise compared to conventional metals.

Contribution

It introduces the exact asymptotic form of the full counting statistics for Dirac fluids, revealing non-Gaussian charge fluctuations in relativistic hydrodynamics.

Findings

Charge noise is parametrically enhanced in Dirac fluids.

The full counting statistics (FCS) is highly non-Gaussian.

The asymptotic form of FCS generalizes previous results for integrable systems.

Abstract

Dirac fluids - interacting systems obeying particle-hole symmetry and Lorentz invariance - are among the simplest hydrodynamic systems; they have also been studied as effective descriptions of transport in strongly interacting Dirac semimetals. Direct experimental signatures of the Dirac fluid are elusive, as its charge transport is diffusive as in conventional metals. In this paper we point out a striking consequence of fluctuating relativistic hydrodynamics: the full counting statistics (FCS) of charge transport is highly non-gaussian. We predict the exact asymptotic form of the FCS, which generalizes a result previously derived for certain interacting integrable systems. A consequence is that, starting from quasi-one dimensional nonequilibrium initial conditions, charge noise in the hydrodynamic regime is parametrically enhanced relative to that in conventional diffusive metals.