Color Superconductivity and Tsallis Statistics

TL;DR

This paper explores how Tsallis non-extensive statistics influence the properties of color superconductivity in high-density quark matter, revealing modifications in the gap, critical temperature, and specific heat behavior.

Contribution

It introduces a generalized framework for color superconductivity using Tsallis statistics and analyzes its effects on the gap equation and thermodynamic properties.

Findings

Generalized universality condition for the gap and critical temperature.

Temperature dependence of the gap varies with Tsallis parameter q.

Specific heat transitions from exponential to linear as q increases.

Abstract

The generalized non-extensive statistics proposed by Tsallis have been successfully utilized in many systems where long range interactions are present. For high density quark matter an attractive long range interaction arising from single gluon exchange suggests the formation of a diquark condensate. We study the effects on this color superconducting phase for two quark flavors due to a change to Tsallis statistics. By numerically solving the gap equation we obtain a generalization of the universality condition, $\frac{2\phi_{0}}{T_{C}}\approx 3.52$ and determine the temperature dependence of the gap. For the Tsallis parameter $q\approx 1$ the specific heat is exponential becoming more linear as q increases. This suggests that for larger values of q s-wave color superconductors behave like high $T_c$ superconductors rather than weak superconductors.