Thermostatistics of the multi-dimensional q-deformed fermionic Newton oscillators

Algin, Abdullah; Arslan, Ebubekir

doi:10.1016/j.physleta.2007.12.050

Cited by 18 publications

(29 citation statements)

References 58 publications

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“…For comparison, we now summarize some of the thermostatistical properties of a gas of the FN-oscillators defined in (1) and (2). In the grand canonical ensemble, the Hamiltonian of such a free FN-oscillators gas has the following form [54]:…”

Section: The Fn-oscillatorsmentioning

confidence: 99%

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A Comparative Study on q-Deformed Fermion Oscillators

Algin

2011

Int J Theor Phys

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In this paper, the algebras, representations, and thermostatistics of four types of fermionic q-oscillator models, called fermionic Newton (FN), Chaichian-Kulish-Ng (CKN), Parthasarathy-Viswanathan-Chaichian (PVC), Viswanathan-Parthasarathy-JagannathanChaichian (VPJC), are discussed. Similarities and differences among the properties of these models are revealed. Particular emphasis is given to the VPJC-oscillators model so that its Fock space representation is analyzed in detail. Possible physical applications of these models are concisely pointed out.

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Section: The Fn-oscillatorsmentioning

confidence: 99%

“…which gives all of the thermodynamical functions in terms of the deformation parameter q. Following the standard procedure [55][56][57], we can determine the equation of state and the particle density for the FN-oscillators gas as follows [54]:…”

Section: The Fn-oscillatorsmentioning

confidence: 99%

A Comparative Study on q-Deformed Fermion Oscillators

Algin

2011

Int J Theor Phys

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“…There have been some discussions about the thermal statistics of various fermionic q-oscillators [14,30,39,42], all of which are focused on the noninteracting systems. Here we give a systematic discussion about the thermodynamics of such systems via the partition function.…”

Section: B Thermodynamicsmentioning

confidence: 99%

q-deformed fermion in many-particle systems and its application to BCS theory

Hou¹,

Huang²,

He³

et al. 2018

J. Stat. Mech.

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In recent decades, there have been increasing interests in quantum statistics beyond the standard Fermi-Dirac and Bose-Einstein statistics, such as the fractional statistics, quon statistics, anyon statistics and quantum groups, since they can provide some new insights into the cosmology, nuclear physics and condensed matter. In this paper, we study the many-particle system formed by the q-deformed fermions (q-fermion), which is realized by deforming the quantum algebra of the anticommutation relations. We investigate from a standard perspective of the finite temperature field theory and try to construct the finite temperature Green's function formalism for the free many-q-fermion system, then generalize it to the well known interacting fermionic system, the superconductor, and finally obtain a consistent q-deformed BCS (qBCS) theory. At low temperature, this theory predicts a Sarma-like ordered phase, and we call it the q-deformed Sarma phase. It also presents a symmetric phase diagram in the parameter space and new thermodynamic relations.

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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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Thermostatistics of the multi-dimensional q-deformed fermionic Newton oscillators

Cited by 18 publications

References 58 publications

A Comparative Study on q-Deformed Fermion Oscillators

A Comparative Study on q-Deformed Fermion Oscillators

q-deformed fermion in many-particle systems and its application to BCS theory

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

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