Dynamic density correlations in a baryon rich fluid using Mori-Zwanzig-Nakjima projection operator method

TL;DR

This paper calculates dynamic density correlations in a baryon-rich fluid near the critical point using the Mori-Zwanzig-Nakajima projection operator method, revealing how viscosities and conductivities influence sound attenuation and thermal diffusivity.

Contribution

It derives hydrodynamic density correlation functions and estimates their behavior near the critical point, incorporating critical exponents from the statistical bootstrap model.

Findings

Bulk viscosity affects sound attenuation as |t|^{-5/4}.

Thermal conductivity influences both sound attenuation and thermal diffusivity.

Results have implications for detecting the QCD critical point in heavy-ion collisions.

Abstract

In this work, we calculate the dynamic density correlations using Mori-Zwanzig-Nakajima projection operator method. With a judicious choice of slow variables we derive the evolution equations for these slow variables starting from generalised Langevin equation. We get the hydrodynamic form of density correlations function which consist of two acoustic peaks: also called Brillouin peaks, and one thermal peak: also called Rayleigh peak. We then estimate the dynamic density correlations near the critical point using critical exponents extracted from the statistical bootstrap model of hadronic matter. We find that the bulk viscosity contributes to the sound attenuation at leading order $\sim|t|^{-\frac{5}{4}}$ while the thermal conductivity contribute at sub-leading order $\sim|t|^{-\frac{3}{4}}$. On the other hand, only the thermal conductivity contributes at leading order $\sim|t|^{\frac{1}{4}}$ to the thermal diffusivity. We discuss the implications of these results in a search for the QCD critical point in the heavy-ion collision experiments.