Bose Gases In Deformed Algebra

Abstract

This thesis explores the impact of the Dunkl formalism, a mathematical framework incorp orating a reflection term controlled by the Wigner parameter θ , on quantum statistical mechanics, particularly Bose-Einstein condensation (BEC) and related phenomena. It examines how Dunkl mo dification alters the prop erties of an ideal Bose gas, including statistical and thermo dynamic b ehaviors, and mo difies blackb o dy radiation, such as the Stefan-Boltzmann law. The research extends to BEC in harmonic and p ower-law traps, showing how θ influences critical temp eratures, condensate fractions, and thermo dynamic prop erties like sp ecific heat capacity. Key findings highlight mo dified thermo dynamic relations, invariant quantities under Dunkl transformation, and unique scaling b ehaviors, demonstrating the formalism’s p otential for advancing understanding of quantum systems and their applications. french