Transport coefficients in a finite volume Polyakov--Nambu--Jona-Lasinio model

TL;DR

This paper investigates how finite system size influences transport coefficients like shear viscosity and electrical conductivity within the Polyakov-Nambu-Jona-Lasinio model, revealing size-dependent behaviors at low temperatures and some size independence at high temperatures.

Contribution

It introduces a finite size framework into the PNJL model to study transport coefficients, incorporating a quantum mechanical momentum cut-off and analyzing size effects across temperature ranges.

Findings

Transport coefficients increase as system size decreases at low temperatures.

At high temperatures, shear viscosity and electrical conductivity become size-independent.

Bulk viscosity exhibits non-trivial size dependence at high temperatures.

Abstract

Finite size consideration of matter significantly affects transport coefficients like shear viscosity, bulk viscosity, electrical conductivity, which we have investigated here in the framework of the Polyakov-Nambu-Jona-Lasinio model. Owing to the basic quantum mechanics, a non-zero lower momentum cut-off is implemented in momentum integrations, used in the expressions of constituent quark masses and transport coefficients. When the system size decreases, the values of these trans- port coefficients are enhanced in low temperature range. At high temperature domain, shear viscos- ity and electrical conductivity become independent of system sizes. Whereas, bulk viscosity, which is associated with scale violating quantities of the system, faces some non-trivial size dependence in this regime. In the phenomenological direction, our microscopic estimations can also be linked with the macroscopic outcome, based on dissipative hydrodynamical simulation.