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arXiv:2006.04392 · Journal of Statistical Mechanics Theory and Experiment

Thermostatistics of a q -deformed relativistic ideal Fermi gas

Xu-Yang Hou, Haiyang Yan, Hao Guo

Published Nov 1, 2020• 9 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1742-5468/abc1ea

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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 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.
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.
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.
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.
During the last three decades, nonstandard statistics for indistinguishable quantum particles has attracted wide attention and research interests from many institutions. Among these new types of statistics, the [Formula: see text]-deformed Bose and Fermi statistics, originated from the study of quantum algebra, are being applied in more and more physical systems. In this paper, we construct a [Formula: see text]-deformed generalization of the BCS-Leggett theory for ultracold Fermi gases based on our previously constructed [Formula: see text]-deformed BCS theory. Some interesting features of this [Formula: see text]-deformed interacting quantum gas are obtained by numerical analysis. For example, in the ordinary Bose–Einstein Condensation regime, the gas presents a fermionic feature instead of bosonic feature if the deformation parameter is tuned suitably, which might be referred to as the [Formula: see text]-induced “Bose–Fermi” crossover. Conversely, a weak sign of the “Fermi–Bose” crossover is also found in the ordinary weak fermionic regime.
Starting with a deformed fermionic grand partition function, we study the high and low temperature thermostatistical properties of a special q -deformed fermion gas in two spatial dimensions. Many of the deformed thermostatistical functions such as the specific heat and the entropy are derived in terms of the real deformation parameter q for the range q < 1. For high temperatures, we specifically focus on the behavior of both the entropy function and the deformed virial coefficients in the equation of state for the q -fermion gas in two dimensions. Possible physical applications of the present q -fermion gas are briefly discussed.