Dissipation in 2D degenerate gases with non-vanishing rest mass

TL;DR

This paper derives transport coefficients for 2D relativistic degenerate gases using kinetic theory, compares models, and analyzes temperature-dependent transport properties across different regimes.

Contribution

It provides a comprehensive derivation and comparison of transport coefficients in 2D relativistic degenerate gases, highlighting the limitations of the Marle model.

Findings

Marle model shows drawbacks compared to Anderson-Witting and Boltzmann results.

Analytical expressions for thermal conductivity, bulk, and shear viscosities are obtained.

Temperature dependence of transport coefficients is analyzed across various regimes.

Abstract

The complete set of transport coefficients for two dimensional relativistic degenerate gases is derived within a relaxation approximation in kinetic theory, by considering both the particle and energy frames. A thorough comparison between Marle and Anderson-Witting's models is carried out, pointing out the drawbacks of the former when compared both to the latter and to the full Boltzmann equation results in the non-degenerate limit. Such task is accomplished by solving the relativistic Uehling-Uhlenbeck equation, in both the particle and energy frames, in order to establish the constitutive equations for the heat flux and the Navier tensor together with analytical expressions for the transport coefficients in such representations. In particular, the temperature dependence of the thermal conductivity (associated with a generalized thermal force) and the bulk and shear viscosities are analyzed and compared within both models and with the non-degenerate, non-relativistic and ultra-relativistic limits.