Bose–Einstein condensation in low dimensional systems with deformed bosons

Algin, Abdullah; Olkun, Ali

doi:10.1016/j.aop.2017.05.021

Cited by 9 publications

(8 citation statements)

References 68 publications

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“…Condensation of some generalized statistics has been investigated by several authors [28,31,[42][43][44]. We consider the condensation of dual statistics in this section in more detail.…”

Section: Condensation Of Dual Statisticsmentioning

confidence: 99%

Thermodynamic geometry, transition between attractive and repulsive interactions and condensation of dual statistics

Ebadi¹,

Mohammadzadeh²,

Mogaddam³

et al. 2020

J. Stat. Mech.

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We consider new generalized statistics based on the generalization of statistical weight. We work out the thermodynamic curvature of an ideal gas with particles obeying such generalized statistics. For different values of generalization parameters; p and q, we observe that both attractive and repulsive intrinsic statistical interaction is expected. As long as p q, the thermodynamic curvature is positive in full physical range. We show that for p < q, generally dominant behavior in high temperature is Fermi-like while in low temperature, the thermodynamic curvature is positive and the systems behaves such as bosons. Also, by more decreasing of the temperature, the system transits to the condensate phase. In fact, the attractive statistical interaction is related to parameter p, while by increasing the value of q, the repulsive interaction is induced. Explicitly, the specified fugacity (z = z * p,q ) of the system, where the sign of thermodynamic curvature is changed and for z < z * p,q (z > z * p,q ) the statistical behavior is fermion like (boson like ), is explored. Also, we extract the variation of statistical behavior of the system for different values of generalization parameters with respect

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“…Condensation of some generalized statistics has been investigated by several authors [28,31,[42][43][44]. We consider the condensation of dual statistics in this section in more detail.…”

Section: Condensation Of Dual Statisticsmentioning

confidence: 99%

Thermodynamic geometry, transition between attractive and repulsive interactions and condensation of dual statistics

Ebadi¹,

Mohammadzadeh²,

Mogaddam³

et al. 2020

J. Stat. Mech.

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“…It is shown that the statistical distribution corresponding to various q-deformation schemes are in fact various Gentile distributions with different maximum occupation numbers q [46]. There are many physical systems obey intermediate statistics, for example, spin waves, or, magnons, which is the elementary excitation of the Heisenberg magnetic system [47], deformed fermion gases [48,49], and deformed boson gases [50]. Moreover, there are also generalizations for Gentile statistics, in which the maximum occupation numbers of different quantum states take on different values [51].…”

Section: The Canonical Partition Function Of Ideal Gentile Gasesmentioning

confidence: 99%

Canonical partition functions: ideal quantum gases, interacting classical gases, and interacting quantum gases

Zhou

Dai

2018

J. Stat. Mech.

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In statistical mechanics, for a system with fixed number of particles, e.g., a finite-size system, strictly speaking, the thermodynamic quantity needs to be calculated in the canonical ensemble. Nevertheless, the calculation of the canonical partition function is difficult. In this paper, based on the mathematical theory of the symmetric function, we suggest a method for the calculation of the canonical partition function of ideal quantum gases, including ideal Bose, Fermi, and Gentile gases. Moreover, we express the canonical partition functions of interacting classical and quantum gases given by the classical and quantum cluster expansion methods in terms of the Bell polynomial in mathematics. The virial coefficients of ideal Bose, Fermi, and Gentile gases is calculated from the exact canonical partition function. The virial coefficients of interacting classical and quantum gases is calculated from the canonical partition function by using the expansion of the Bell polynomial, rather than calculated from the grand canonical potential.

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“…The corresponding quantum algebras are now actively used to analyze complex physical systems [20]. For example, the thermodynamics of Bose systems and the phenomenon of the Bose condensation were studied with their help in works [21,22]. In work [23], it was shown how the structure of particles and the inter-action between them can be efficiently taken into account by means of μ-and 𝑞-deformed bosons.…”

Section: Introductionmentioning

confidence: 99%

Ideal Bose Gas in Some Deformed Types of Thermodynamics. Correspondence between Deformation Parameters

Chubai

Rovenchak

2020

Ukr. J. Phys.

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Two approaches to the construction of thermodynamics in the framework of the q- and м-formalisms, which correspond to certain deformations of the algebra of the creation–annihilation operators, have been considered. By comparing the obtained results, an approximate, independent of the space dimension, correspondence was revealed between the second virial coefficients for the ideal q- and м-deformed Bose gases. The corresponding discrepancy arises only at the level of the third virial coefficient. A method for emulating the м-deformed Bose gas up to the third virial coefficient inclusive by means of the two-parametric nonadditive Polychronakos statistics is demonstrated.

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Bose–Einstein condensation in low dimensional systems with deformed bosons

Cited by 9 publications

References 68 publications

Thermodynamic geometry, transition between attractive and repulsive interactions and condensation of dual statistics

Thermodynamic geometry, transition between attractive and repulsive interactions and condensation of dual statistics

Canonical partition functions: ideal quantum gases, interacting classical gases, and interacting quantum gases

Ideal Bose Gas in Some Deformed Types of Thermodynamics. Correspondence between Deformation Parameters

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