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arXiv:quant-ph/9912111 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Thermostatistics of aq-deformed boson gas

A. Lavagno, P. Narayana Swamy

Published Feb 1, 2000• 111 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreve.61.1218

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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.
We study the thermostatistics of q-deformed bosons and fermions obeying the symmetric (q<-->q(-1)) algebra and show that it can be built on the formalism of q calculus. The entire structure of thermodynamics is preserved if ordinary derivatives are replaced by an appropriate Jackson derivative. In this framework, we derive the most important thermodynamic functions describing the q-boson and q-fermion ideal gases in the thermodynamic limit. We also investigate the semiclassical limit and the low-temperature regime and demonstrate that the nature of the q deformation gives rise to pure quantum statistical effects stronger than undeformed boson and fermion particles.
Based on the q-deformed oscillator algebra, we study the behavior of the mean occupation number and its analogies with intermediate statistics and we obtain an expression in terms of an infinite continued fraction, thus clarifying successive approximations. In this framework, we study the thermostatistics of q-deformed bosons and fermions and show that thermodynamics can be built on the formalism of q-calculus. The entire structure of thermodynamics is preserved if ordinary derivatives are replaced by the use of an appropriate Jackson derivative and q-integral. Moreover, we derive the most important thermodynamic functions and we study the q-boson and q-fermion ideal gas in the thermodynamic limit.
It is known from the early work of May in 1964 that ideal Bose gas do not exhibit condensation phenomenon in two dimensions. On the other hand, it is also known that the thermostatistics arising from q-deformed oscillator algebra has no connection with the spatial dimensions of the system. Our recent work concerns the study of important thermodynamic functions such as the entropy, occupation number, internal energy and specific heat in ordinary three spatial dimensions, where we established that such thermostatistics is developed by consistently replacing the ordinary thermodynamic derivatives by the Jackson derivatives. The thermostatistics of q-deformed bosons and fermions in two spatial dimensions is an unresolved question that is the subject of this investigation. We study the principal thermodynamic functions of both bosons and fermions in the two-dimensional q-deformed formalism and we find that, different from the standard case, the specific heat of q-boson and q-fermion ideal gas, at fixed temperature and number of particles, are no longer identical.
It is known from the early work of May in 1964 that ideal Bose gas do not exhibit condensation phenomenon in two dimensions. On the other hand, it is also known that the thermostatistics arising from q-deformed oscillator algebra has no connection with the spatial dimensions of the system. Our recent work concerns the study of important thermodynamic functions such as the entropy, occupation number, internal energy and specific heat in ordinary three spatial dimensions, where we established that such thermostatistics is developed by consistently replacing the ordinary thermodynamic derivatives by the Jackson derivatives. The thermostatistics of q-deformed bosons and fermions in two spatial dimensions is an unresolved question that is the subject of this investigation. We study the principal thermodynamic functions of both bosons and fermions in the two-dimensional q-deformed formalism and we find that, different from the standard case, the specific heat of q-boson and q-fermion ideal gas, at fixed temperature and number of particles, are no longer identical.
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.
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.