A Hydrodynamic Theory for Non-Equilibrium Full Counting Statistics in One-Dimensional Quantum Systems

TL;DR

This paper develops a hydrodynamic framework to describe non-equilibrium charge fluctuations in one-dimensional quantum systems after a quench, linking microscopic fluctuations to macroscopic hydrodynamic quantities.

Contribution

It introduces a simple hydrodynamic expression for full counting statistics in quantum quenches, valid under specific physical conditions, and verifies its accuracy through free fermion models.

Findings

The hydrodynamic formula accurately predicts first cumulants of charge fluctuations.

Explicit conditions for the applicability of hydrodynamic theory are identified.

Cross-checks with exact free fermion results validate the approach.

Abstract

We study the dynamics of charge fluctuations after homogeneous quantum quenches in one-dimensional systems with ballistic transport. For short but macroscopic times where the non-trivial dynamics is largely dominated by long-range correlations, a simple expression for the associated full counting statistics can be obtained by hydrodynamic arguments. This formula links the non-equilibrium charge fluctuation after the quench to the fluctuations of the associated current after a charge-biased inhomogeneous modification of the original quench which corresponds to the paradigmatic partitioning protocol. Under certain assumptions, the fluctuations in the latter case can be expressed by explicit closed form formulas in terms of thermodynamic and hydrodynamic quantities via the Ballistic Fluctuations Theory. In this work, we identify precise physical conditions for the applicability of a fully hydrodynamic theory, and provide a detailed analysis explicitly demonstrating how such conditions are met and how this leads to such hydrodynamic treatment. We discuss these conditions at length in non-relativistic free fermions, where calculations become feasible and allow for cross-checks against exact results. In physically relevant cases, strong long-range correlations can complicate the hydrodynamic picture, but our formula still correctly reproduces the first cumulants.