Linearized fluctuating hydrodynamics via random polynomials

TL;DR

This paper models hydrodynamic dispersion relations as polynomials with random coefficients to incorporate thermal fluctuations, revealing that fluctuations significantly alter the analytic structure of these relations and support persistent hydrodynamic behavior.

Contribution

It introduces a novel approach to understanding hydrodynamic dispersion relations through random polynomials, highlighting the impact of thermal fluctuations on their analytic structure.

Findings

Distribution of roots differs from deterministic cases.

Imaginary parts of poles are notably affected by fluctuations.

Hydrodynamic behavior persists and is enhanced by fluctuations.

Abstract

We argue that an ensemble of backgrounds best understands hydrodynamic dispersion relations in a medium with few degrees of freedom and is therefore subject to strong thermal fluctuations. In the linearized regime, dispersion relations become describeable by polynomials with random coefficients. We give a short review of this theory and perform a numerical study of the distribution of the roots of polynomials whose coefficients are of the order of a Knudsen series but fluctuate in accordance with canonical fluctuations of temperature. We find that, remarkably, the analytic structure of the poles of fluctuating dispersion relations is very different from deterministic ones, particularly regarding the distribution of imaginary parts with respect to real components. We argue that this provides evidence that hydrodynamic behavior persists, and is enhanced, by non-perturbative background fluctuations.