On Dunkl-Bose-Einstein Condensation in Harmonic Traps

TL;DR

This paper investigates Bose-Einstein condensation of an ideal Bose gas in a harmonic trap using Dunkl formalism, deriving critical temperature, ground state population, and thermal quantities, and comparing with traditional results.

Contribution

It introduces a novel application of Dunkl formalism to analyze Bose-Einstein condensation in harmonic traps, providing analytic expressions and improved experimental-theoretical agreement.

Findings

Derived an analytic expression for the critical temperature.

Compared Dunkl formalism results with traditional case.

Explored Dunkl-internal energy and heat capacity functions.

Abstract

The use of the Dunkl derivative, which is defined by a combination of the difference-differential and reflection operator, allows the classification of the solutions according to even and odd solutions. Recently, we considered the Dunkl formalism to investigate the Bose-Einstein condensation of an ideal Bose gas confined in a gravitational field. In this work, we address a similar problem and examine an ideal Bose gas trapped by a three-dimensional harmonic oscillator within the Dunkl formalism. To this end, we derive an analytic expression for the critical temperature of the N particle system, discuss its value at large-N limit and finally derive and compare the ground state population with the usual case result. In addition, we explore two thermal quantities, namely the Dunkl-internal energy and the Dunkl-heat capacity functions. The Wigner parameter of the Dunkl formalism can be successfully used to obtain a better agreement between experimental and theoretical results.