Effect of quantum group invariance on trapped Fermi gases

TL;DR

This paper investigates how quantum group symmetry influences the thermodynamic properties of trapped Fermi gases, including chemical potential, heat capacity, and spatial distribution, with additional analysis of interaction effects on ground state energy.

Contribution

It introduces the study of quantum group invariance in Fermi gases and computes thermodynamic and ground state properties considering quantum group parameters and interactions.

Findings

Chemical potential depends on quantum group parameter q and dimensions D

Heat capacity and spatial distribution are affected by quantum group symmetry

Ground state energy is modified by fourth-order quantum group interactions

Abstract

We study the properties of a thermodynamic system having the symmetry of a quantum group and interacting with a harmonic potential. We calculate the dependence of the chemical potential, heat capacity and spatial distribution of the gas on the quantum group parameter $q$ and the number of spatial dimensions $D$. In addition, we consider a fourth-order interaction in the quantum group fields $\Psi$, and calculate the ground state energy up to first order.