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

Algin, Abdullah; Arslan, Ebubekir

doi:10.1088/1751-8113/41/36/365006

Cited by 14 publications

(4 citation statements)

References 85 publications

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“…as the basis of some other works by many authors, e.g., [38,39,40,41,42,43,44]. Moreover, such a treatment also appears in other literature [45,46,47,48,49,50]. In fact, some authors had noticed that the distribution obtained by such a way is not properly the distribution of the average occupation number [43].…”

Section: The Q-deformation Distributionsmentioning

confidence: 83%

“…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%

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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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Section: The Q-deformation Distributionsmentioning

confidence: 83%

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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“…On the other hand, the above comparison may also be physically important, since some recent studies with o ne deformation parameter similarly adduced some values for the deformation parameter [81,82]. Hence, one can also view two parameter deformations as a phenomenological means of introducing extra parameters, " 1 q , 2 q ", to account for some non-linear properties in the system.…”

Section: Sumentioning

confidence: 99%

Bose–Einstein condensation in a gas of Fibonacci oscillators

Algin¹

2008

J. Stat. Mech.

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“…Also, some recent studies have been used to view q-deformations as phenomenological means of introducing an extra parameter, "q", to account for non-linearity in the system. Such an approach was considered in [56,57], where some values of q are found to fit the properties of a real (nonideal) laser and of the gap in the specific heat of a dilute gas of rubidium atoms, respectively. Therefore, such interesting results constitute some motivation to consider quantum algebras for approximating properties of interpolating statistics.…”

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confidence: 99%

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

Cited by 14 publications

References 85 publications

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

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

Bose–Einstein condensation in a gas of Fibonacci oscillators

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

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