Bose-Einstein condensation of a quantum group gas

TL;DR

This paper investigates how quantum group symmetries, specifically $SU_q(2)$, influence Bose-Einstein condensation, revealing that these symmetries enhance condensation and cause discontinuities in heat capacity at the critical temperature.

Contribution

It demonstrates that quantum group symmetries modify Bose-Einstein condensation, increasing the critical temperature and heat capacity gap, which is a novel insight into quantum gas behavior.

Findings

Quantum group symmetry enhances Bose-Einstein condensation.

Discontinuity in heat capacity at the critical temperature.

Critical temperature and heat capacity gap increase with $q$ and plateau for $q>3$.

Abstract

We study the Bose-Einstein condensation of a gas with $SU_q(2)$ symmetry. We show, in the thermodynamic limit, that the boson interactions introduced by the quantum group symmetries enhance Bose-Einstein condensation giving a discontinuity in the heat capacity $C_v$ at the critical temperature $T_c$. The critical temperature and the gap in $C_v$ increase with the value of the parameter $q$ and become approximately constant for $q>3$.