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arXiv:0810.1827 · Journal of Physics A Mathematical and Theoretical

Bose–Einstein condensation in a gas of the bosonic Newton oscillators

Abdullah Algin, Emine Arslan

Published Aug 5, 2008• 17 citations
arXivHTMLPDF

Abstract

The multi-dimensional q -deformed bosonic Newton oscillator algebra with U ( d )-symmetry is considered. The high- and low-temperature thermostatistical properties of a gas of the q -deformed bosonic Newton oscillators are obtained in the thermodynamical limit. It is shown that the Bose–Einstein condensation occurs in such a gas for values of the real deformation parameter q smaller than 1. However, the ordinary boson gas results can be recovered in the limit q = 1.

DOI
10.1088/1751-8113/41/36/365006

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The multi-dimensional q -deformed bosonic Newton oscillator algebra with U ( d )-symmetry is considered. The high- and low-temperature thermostatistical properties of a gas of the q -deformed bosonic Newton oscillators are obtained in the thermodynamical limit. It is shown that the Bose–Einstein condensation occurs in such a gas for values of the real deformation parameter q smaller than 1. However, the ordinary boson gas results can be recovered in the limit q = 1.
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The thermostatistical properties of an ideal gas of q -deformed bosons trapped in a D -dimensional power-law potential are studied, based on the q -deformed Bose–Einstein distribution. The effects of q -deformation on the properties of the system are discussed. It is shown that q -deformed bosons ( q ≠ 1) possess many different characteristics from those of ordinary bosons, which include the condition that Bose–Einstein condensation (BEC) occurs, the critical temperature and the continuity of heat capacity.
The q -deformed Bose–Einstein distribution derived from the q -boson algebra is used to study the low-temperature behavior of an ideal q -deformed Bose gas with relativistic energy spectrum. The effects of q -deformation on the properties relative to Bose–Einstein condensation (BEC) are discussed. It is shown that q -deformation leads to some novel characteristics different from those of an original Bose gas, which include the criteria on the occurrence of BEC, critical temperature and jump of heat capacity at the critical point. The results obtained here provide a unified description for the properties of q -deformed Bose systems from the nonrelativistic case to the ultrarelativistic limit, so that some important conclusions in the literature are included in this paper.
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 θ\thetaθ θ in the range θ>0\theta > 0θ>0 θ > 0 . As another application of the DDBE statistics, we investigate the thermostatistics of the Dunkl-deformed Debye solid and the effects of the deformation parameter θ\thetaθ θ 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.
The q-deformed Bose–Einstein distribution is used to study the Bose–Einstein condensation (BEC) of a q-deformed Bose gas in random box. It is shown that the BEC transition temperature is lowered due to random boundary conditions. The effects of q-deformation on the properties of the system are also discussed. We find some properties of a q-deformed Bose gas, which are different from those of an ordinary Bose gas. Similar results are also shown for q-bosons confined in a harmonic oscillator potential well.
We show that a natural realization of the thermostatistics of q bosons can be built on the formalism of q calculus, and that the entire structure of thermodynamics is preserved if we use an appropriate Jackson derivative in place of the ordinary thermodynamics derivative. This framework allows us to obtain a generalized q boson entropy which depends on the q basic number. We study the ideal q boson gas in the thermodynamic limit which is shown to exhibit Bose-Einstein condensation with a higher critical temperature and a discontinuous specific heat.