Thermostatistic properties of a<i>q</i>-deformed ideal Fermi gas with a general energy spectrum

Cai, Shukuan; Su, Guozhen; Chen, Jincan

doi:10.1088/1751-8113/40/37/003

Cited by 29 publications

(41 citation statements)

References 40 publications

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“…Similar Hamiltonians were also considered by several other authors [30][31][32][33][34][35][36][37][38][39][40][41][67][68][69][70][71][72][73]75,76]. We should concisely point out that the form in Eq.…”

Section: High Temperature Thermostatistics Of the Vpjc-oscillatorssupporting

confidence: 58%

High-temperature behavior of a deformed Fermi gas obeying interpolating statistics

Algin

Şenay

2012

Phys. Rev. E

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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.

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Section: High Temperature Thermostatistics Of the Vpjc-oscillatorssupporting

confidence: 58%

High-temperature behavior of a deformed Fermi gas obeying interpolating statistics

Algin

Şenay

2012

Phys. Rev. E

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“…Concretely, a key step in the derivation of the statistical distribution is to deal with the average value f (N ) , where f (N ) is a function of N . In the literature [37], however, such an average value is approximately taken as f (N ) ≃ f ( N ), or, for more details, in the literature the authors take the approximation q N ≃ q N [38,39,40,41,42,43,44,45,46,47,48,49,50]. taking such a replacement, as stated in the literature [51,52,53], is that N gives a nondeformed Bose-Einstein distribution.…”

Section: Parametermentioning

confidence: 99%

Calculating statistical distributions from operator relations: The statistical distributions of various intermediate statistics

Dai

Xie

2012

Annals of Physics

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In this paper, we give a general discussion on the calculation of the statistical distribution from a given operator relation of creation, annihilation, and number operators. Our result shows that as long as the relation between the number operator and the creation and annihilation operators can be expressed as a † b = Λ (N ) or N = Λ −1 a † b , where N , a † , and b denote the number, creation, and annihilation operators, i.e., N is a function of quadratic product of the creation and annihilation operators, the corresponding statistical distribution is the Gentile distribution, a statistical distribution in which the maximum occupation number is an arbitrary integer. As examples, we discuss the statistical distributions corresponding to various operator relations. In particular, besides Bose-Einstein and Fermi-Dirac cases, we discuss the statistical distributions for various schemes of intermediate statistics, especially various q-deformation schemes. Our result shows that the statistical distributions corresponding to various q-deformation schemes are various Gentile distributions with different maximum occupation numbers which are determined by the deformation parameter q. This result shows that the results given in much literature on the q-deformation distribution are inaccurate or incomplete. *

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“…Many-particle systems consisting of bosons, fermions and anyons have been exhaustively studied. One may also be interested in the properties of many-quon systems [34][35][36][37][38][39][40][41][42][43]. There have been some studies on the thermodynamics of non-interacting many-q-boson and many-q-fermion systems.…”

Section: Introductionmentioning

confidence: 99%

Finite temperature behaviors of q-deformed Fermi gases

et al. 2019

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During the last three decades, non-standard statistics for indistinguishable quantum particles has attracted broad attentions and research interests from many institutions. Among these new types of statistics, the qdeformed 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 q-deformed generalization of the BCS-Leggett theory for ultracold Fermi gases based on our previously constructed q-deformed BCS theory. Some interesting features of this q-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 q-induced "Bose-Fermi" crossover. Conversely, a weak sign of the "Fermi-Bose" crossover is also found in the ordinary weak fermionic regime.

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

Cited by 29 publications

References 40 publications

High-temperature behavior of a deformed Fermi gas obeying interpolating statistics

High-temperature behavior of a deformed Fermi gas obeying interpolating statistics

Calculating statistical distributions from operator relations: The statistical distributions of various intermediate statistics

Finite temperature behaviors of q-deformed Fermi gases

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