Relativistic Theory of Hydrodynamic Fluctuations with Applications to Heavy Ion Collisions

TL;DR

This paper develops a relativistic hydrodynamic fluctuation theory for high-energy heavy ion collisions, revealing how sound modes induce long-range correlations and providing a method to infer viscosities from experimental data.

Contribution

It introduces a novel relativistic fluctuation framework and analyzes sound mode effects on correlations in expanding hydrodynamic systems relevant to heavy-ion collisions.

Findings

Long-range rapidity correlations are generated by sound modes.

Expansion causes non-linear dispersion and attenuation of sound modes.

Two-particle correlators can potentially measure viscosities.

Abstract

We develop the relativistic theory of hydrodynamic fluctuations for application to high energy heavy ion collisions. In particular, we investigate their effect on the expanding boost-invariant (Bjorken) solution of the hydrodynamic equations. We discover that correlations over a long rapidity range are induced by the propagation of the sound modes. Due to the expansion, the dispersion law for these modes is non-linear and attenuated even in the limit of zero viscosity. As a result, there is a non-dissipative wake behind the sound front which is generated by any instantaneous point-like fluctuation. We evaluate the two-particle correlators using the initial conditions and hydrodynamic parameters relevant for heavy-ion collisions at RHIC and LHC. In principle these correlators can be used to obtain information about the viscosities because the magnitudes of the fluctuations are directly proportional to them.