Thermostatistics of the Dunkl-deformed boson gas: algebra, Fock space, condensation, and Debye crystal model

Abstract Based on the framework established in a recent work (Ubriaco in Physica A 414:128, 2014), wherein a generalized bosonic model was formulated using the Dunkl operator formalism (DOF), we extend this approach to its different applications with introducing a statistical distribution—termed the Dunkl-deformed Bose–Einstein (DDBE) distribution—constructed by generalizing the usual Bose–Einstein distribution through the DOF. In this framework, we study further general thermodynamical and statistical properties of a gas model of the Dunkl-deformed bosons obeying the DDBE statistics. Emphasis is given to a careful analysis on the conditions under which the Bose–Einstein-like condensation would occur in the present Dunkl-deformed boson gas. It is shown that the critical temperature for such a system is higher than that of the usual (undeformed) Bose gas for values of the model deformation parameter $$\theta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>θ</mml:mi> </mml:math> in the range $$\theta &gt; 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>θ</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> . As another application of the DDBE statistics, we investigate the thermostatistics of the Dunkl-deformed Debye solid and the effects of the deformation parameter $$\theta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>θ</mml:mi> </mml:math> on the high- and low-temperature behavior of the model specific heat are discussed. Our results obtained in this study could provide much physical insight for approaching not only in the treatment of interacting bosons theories including collective excitations, but also in the condensation characteristics of quantum systems beyond the standard formalism.