Fluctuation dynamics in a relativistic fluid with a critical point

TL;DR

This paper develops a relativistic fluctuation formalism for fluids near the QCD critical point, revealing how fluctuations influence transport coefficients and extend existing models.

Contribution

It introduces a comprehensive relativistic fluctuation framework that incorporates feedback effects and nonlocal terms, extending the Hydro+ approach.

Findings

Calculated universal non-analytic frequency dependence of transport coefficients.

Demonstrated the formalism's consistency with and extension of Hydro+ near the critical point.

Provided cutoff-independent equations suitable for numerical simulations.

Abstract

To describe dynamics of bulk and fluctuations near the QCD critical point we develop general relativistic fluctuation formalism for a fluid carrying baryon charge. Feedback of fluctuations modifies hydrodynamic coefficients including bulk viscosity and conductivity and introduces nonlocal and non-instantaneous terms in constitutive equations. We perform necessary ultraviolet (short-distance) renormalization to obtain cutoff independent deterministic equations suitable for numerical implementation. We use the equations to calculate the universal non-analytic small-frequency dependence of transport coefficients due to fluctuations (long-time tails). Focusing on the critical mode we show how this general formalism matches existing Hydro+ description of fluctuations near the QCD critical point and nontrivially extends it inside and outside of the critical region.