Ideal Bose Gas and Blackbody Radiation in the Dunkl Formalism

TL;DR

This paper explores how the Dunkl formalism, a deformation involving difference-differential and reflection operators, affects the thermodynamics of ideal Bose gases and blackbody radiation, revealing modifications in key physical quantities.

Contribution

It introduces a novel approach linking Dunkl formalism with quantum statistical systems, deriving new expressions for thermodynamic properties and analyzing their behavior.

Findings

Dunkl-condensation temperature increases with parameter θ

Total radiated energy in blackbody radiation is modified by Dunkl formalism

Entropy and specific heat increase due to Dunkl deformation

Abstract

Recently, deformed quantum systems gather lots of attention in the literature. Dunkl formalism differs from others by containing the difference-differential and reflection operator. It is one of the most interesting deformations since it let us discuss the solutions according to the even and odd solutions. In this work, we studied the ideal Bose gas and the blackbody radiation via the Dunkl formalism. To this end, we made a liaison between the coordinate and momentum operators with the creation and annihilation operators which allowed us to obtain the expressions of the partition function, the condensation temperature, and the ground state population of the Bose gas. We found that Dunkl-condensation temperature increases with increasing {\theta} value. In the blackbody radiation phenomena, we found how the Dunkl formalism modifies total radiated energy. Then, we examined the thermal quantities of the system. We found that the Dunkl deformation causes an increase in entropy and specific heat functions as well as in the total radiation energy. However, we observed a decrease in the Dunk-corrected Helmholtz free energy in this scenario. Finally, we found that the equation of state is invariant even in the considered formalism.