Shear viscosity and electrical conductivity of rotating quark matter in Nambu--Jona-Lasinio Model

TL;DR

This paper studies how rotation affects the transport properties of quark matter using the NJL model, revealing anisotropic behavior and Hall-like phenomena induced by rotation.

Contribution

It introduces a modified NJL model with spinorial connections to analyze rotation effects on shear viscosity and electrical conductivity, highlighting anisotropy and non-dissipative Hall-like effects.

Findings

Rotation decreases the chiral condensate, enhancing transport properties.

Rotation induces anisotropy in shear viscosity and electrical conductivity.

Hall-like non-dissipative transport phenomena emerge at zero net quark density.

Abstract

The Lagrangian for strongly interacting and rotating quark matter is modified with the inclusion of the spinorial connections, which in turn affect the thermodynamic equation of state and transport properties of the medium. In this work, we investigate the transport properties of quark matter under finite rotation, focusing specifically on electrical conductivity and shear viscosity by using a two-flavor Nambu--Jona-Lasinio (NJL) model. The chiral condensate in the NJL model decreases under rotation, leading to enhanced transport properties. Moreover, rotation induces anisotropy in the transport coefficients, which are calculated within the kinetic theory framework using the Boltzmann transport equation. The Coriolis force is introduced in the force term of the Boltzmann transport equation, like the Lorentz force, which is considered for finite magnetic fields. By using a phenomenological temperature-dependent angular velocity, we observe that the variation of anisotropic components with temperature preserves the traditional valley-shaped pattern. However, the magnitude of the anisotropic components is suppressed compared to the usual component one finds in the absence of rotation. Interestingly, at zero net quark density, Hall-like transport phenomena emerge as significant non-dissipative contributions under rotation, which is not expected under finite magnetic fields due to the cancellation of quark and anti-quark Hall currents.