Relativistic second-order dissipative hydrodynamics at finite chemical potential

Amaresh Jaiswal,Bengt Friman,Krzysztof Redlich

doi:10.1016/j.physletb.2015.11.018

Amaresh Jaiswal, Bengt Friman + Show 1 more

Open Access

https://doi.org/10.1016/j.physletb.2015.11.018

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Abstract

Starting from the Boltzmann equation in the relaxation time approximation and employing a Chapman–Enskog like expansion for the distribution function close to equilibrium, we derive second-order evolution equations for the shear stress tensor and the dissipative charge current for a system of massless quarks and gluons. The transport coefficients are obtained exactly using quantum statistics for the phase space distribution functions at non-zero chemical potential. We show that, within the relaxation time approximation, the second-order evolution equations for the shear stress tensor and the dissipative charge current can be decoupled. We find that, for large values of the ratio of chemical potential to temperature, the charge conductivity is small compared to the coefficient of shear viscosity. Moreover, we show that in the relaxation-time approximation, the limiting behaviour of the ratio of heat conductivity to shear viscosity is qualitatively similar to that obtained for a strongly coupled conformal plasma.

Highlights

High-energy heavy ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC) [1,2] and the CERN Large Hadron Collider (LHC) [3,4,5] create strongly interacting matter under extreme conditions of high temperature and density as it is believed to have existed in the very early universe [6,7]
In this Letter, we present the derivation of second-order evolution equations for shear stress tensor and dissipative charge current for a system consisting of massless quarks and gluons
The bulk viscous pressure vanishes for such a system and the dissipation is solely due to the shear stress tensor and the dissipative charge current

Summary

Introduction

High-energy heavy ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC) [1,2] and the CERN Large Hadron Collider (LHC) [3,4,5] create strongly interacting matter under extreme conditions of high temperature and density as it is believed to have existed in the very early universe [6,7]. In the presence of conserved charges but for classical particles with vanishing masses, the second-order transport coefficients corresponding to charge diffusion (or alternatively heat conduction) have been obtained by employing the moment method [40,41]. They still remain to be determined for quantum statistics. In order to obtain the form of the non-equilibrium distribution function, we employ a Chapman–Enskog like expansion to iteratively solve the Boltzmann equation in the relaxation time approximation [32] Using this expansion, we derive the first-order constitutive relations and subsequently the second-order evolution equations for the dissipative quantities. We demonstrate that the limiting behaviour of the heat conductivity to shear viscosity ratio, obtained here in the relaxation-time approximation, is qualitatively identical to that of a conformal fluid in the strong coupling limit

Relativistic hydrodynamics

Dissipative evolution equations

Transport coefficients

Conclusions and outlook