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Journal of Physics A Mathematical and Theoretical

Thermostatistic properties of aq-deformed ideal Fermi gas with a general energy spectrum

Shukuan Cai, Guozhen Su, Jincan Chen

Published Aug 29, 2007• 30 citations
Publisher

Abstract

The thermostatistic problems of a q -deformed ideal Fermi gas in any dimensional space and with a general energy spectrum are studied, based on the q -deformed Fermi–Dirac distribution. The effects of the deformation parameter q on the properties of the system are revealed. It is shown that q -deformation results in some novel characteristics different from those of an ordinary system. Besides, it is found that the effects of the q -deformation on the properties of the Fermi systems are very different for different dimensional spaces and different energy spectrums.

DOI
10.1088/1751-8113/40/37/003

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The thermostatistic problems of a q -deformed ideal Fermi gas in any dimensional space and with a general energy spectrum are studied, based on the q -deformed Fermi–Dirac distribution. The effects of the deformation parameter q on the properties of the system are revealed. It is shown that q -deformation results in some novel characteristics different from those of an ordinary system. Besides, it is found that the effects of the q -deformation on the properties of the Fermi systems are very different for different dimensional spaces and different energy spectrums.
The q-deformed Fermi–Dirac distribution derived from the q-fermion algebra is used to study the thermostatistical properties of a q-deformed Fermi gas trapped in a generic power-law potential, and the effects of q-deformation on the properties of the system are discussed. It is shown that q-deformation leads to some novel characteristics compared with those of an original Fermi system. It is found that the effects of q-deformation display different characteristics in the cases of different kinematic characteristics of particles and different shapes of external potentials. The results obtained here present a unified description for the thermostatistical properties of a class of q-deformed as well as original Fermi systems, so that many important conclusions in the literature are included in this paper.
Abstract In this paper, we formulate a q -deformed many-body theory for relativistic Fermi gas and discuss the effects of the deformation parameter q on physical properties of such systems. Since antiparticle excitations appear in the relativistic regime, a suitable treatment to the choice of deformation parameters for both fermions and antifermions must be carefully taken in order to get a consistent theory. By applying this formulation, we further study the thermostatistic properties of a q -deformed ideal relativistic Fermi gas. It can be shown that even in the noninteracting scenario, the system exhibits interesting characteristics which are significantly different from ordinary Fermi gases. Explicitly, antiparticles may become dominant due to the shift of chemical potential by the deformation parameter q . This may build a solid foundation for further studies of q -deformed relativistic interacting systems. We also apply our model to study the electron gas in a white dwarf. The effect of the deformation parameter on the Chandrasekhar limit is discussed.
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.
An outstanding idea originally introduced by Greenberg is to investigate whether there is equivalence between intermediate statistics, which may be different from anyonic statistics, and q-deformed particle algebra. Also, a model to be studied for addressing such an idea could possibly provide us some new consequences about the interactions of particles as well as their internal structures. Motivated mainly by this idea, in this work, we consider a q-deformed Fermi gas model whose statistical properties enable us to effectively study interpolating statistics. Starting with a generalized Fermi-Dirac distribution function, we derive several thermostatistical functions of a gas of these deformed fermions in the thermodynamical limit. We study the high-temperature behavior of the system by analyzing the effects of q deformation on the most important thermostatistical characteristics of the system such as the entropy, specific heat, and equation of state. It is shown that such a deformed fermion model in two and three spatial dimensions exhibits the interpolating statistics in a specific interval of the model deformation parameter 0 < q < 1. In particular, for two and three spatial dimensions, it is found from the behavior of the third virial coefficient of the model that the deformation parameter q interpolates completely between attractive and repulsive systems, including the free boson and fermion cases. From the results obtained in this work, we conclude that such a model could provide much physical insight into some interacting theories of fermions, and could be useful to further study the particle systems with intermediate statistics.
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.