Bounding the Wigner Deformation Parameter in Harmonically Trapped Bose Gases

TL;DR

This paper investigates how the Wigner deformation parameter affects thermodynamic properties of a harmonically trapped Bose gas, establishing bounds for the parameter while confirming the phase transition's universality.

Contribution

It introduces bounds for the Wigner parameter based on thermodynamic consistency and analyzes its influence on thermodynamic functions without altering the phase transition nature.

Findings

Wigner parameter modifies the slopes of energy and heat capacity near criticality.

Phase transition order and critical exponents remain unchanged by the Wigner deformation.

Thermodynamic bounds for the Wigner parameter are established in different temperature regimes.

Abstract

By examining the internal energy and the heat capacity of a harmonically trapped ideal Bose gas within the Dunkl formalism, we show that the Wigner parameter influences the slopes of these thermodynamic functions in the critical region, reflecting its role in modifying the statistical properties of the system. However, despite these modifications, the phase transition itself retains the same order and critical exponents as in the standard case, in accordance with symmetry arguments. Furthermore, upon analyzing the classical behavior, we establish both upper and lower bounds for the Wigner parameter by ensuring thermodynamic consistency in different temperature regimes.