122. [K. 20. f.] The Fundamental Formulae of Spherical Trigonometry.

Jackson, Cathie

doi:10.2307/3605113

Cited by 29 publications

(47 citation statements)

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“…The transformation from Fock space to the configuration space (Bargmann holomorphic representation) may be accomplished by means of the Jackson derivative (JD) [4,15,16]…”

Section: Q-oscillators Algebra and Thermal Averagesmentioning

confidence: 99%

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Generalized thermodynamics ofq-deformed bosons and fermions

2002

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We study the thermostatistics of q-deformed bosons and fermions obeying the symmetric (q<-->q(-1)) algebra and show that it can be built on the formalism of q calculus. The entire structure of thermodynamics is preserved if ordinary derivatives are replaced by an appropriate Jackson derivative. In this framework, we derive the most important thermodynamic functions describing the q-boson and q-fermion ideal gases in the thermodynamic limit. We also investigate the semiclassical limit and the low-temperature regime and demonstrate that the nature of the q deformation gives rise to pure quantum statistical effects stronger than undeformed boson and fermion particles.

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“…The transformation from Fock space to the configuration space (Bargmann holomorphic representation) may be accomplished by means of the Jackson derivative (JD) [4,15,16]…”

Section: Q-oscillators Algebra and Thermal Averagesmentioning

confidence: 99%

“…The mathematical framework of q-oscillators is based on the q-calculus which is introduced via the Jackson derivative (JD) [4]. We thus expect such a q-calculus to play an important rôle in the thermostatistics of q-oscillators.…”

Section: Introductionmentioning

confidence: 99%

Generalized thermodynamics ofq-deformed bosons and fermions

2002

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“…It is interesting to observe that a similar comparative analysis of the generalized thermostatistic properties of bosons and fermions has been carried out in [69] in the context of the quantum q-deformed algebra. This differs from Tsallis framework in that it relies on the modification of the quantum algebra of the creation and annihilation operators based on the q-calculus [70], rather than the modification of the partitioning of the microstates of the many body system. In that case, it has been shown that q-deformed bosons and fermions have an enhancement of the quantum statistical effects compared to standard behavior.…”

Section: Q-generalized Tsallis Statistics For Neutrino Mixingmentioning

confidence: 99%

Nonextensive Tsallis statistics in Unruh effect for Dirac neutrinos

Luciano¹,

Blasone²

2021

Preprint

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Flavor mixing of quantum fields was found to be responsible for the breakdown of the thermal Unruh effect. Recently, this result was revisited in the context of nonextensive Tsallis thermostatistics, showing that the emergent vacuum condensate can still be featured as a thermal-like bath, provided that the underlying statistics is assumed to obey Tsallis prescription. This was analyzed explicitly for bosons. Here we extend this study to Dirac fermions and in particular to neutrinos. Working in the relativistic approximation, we provide an effective description of the modified Unruh spectrum in terms of the q-generalized Tsallis statistics, the q-entropic index being dependent on the mixing parameters sin θ and ∆m. As opposed to bosons, we find q > 1, which is indicative of the subadditivity regime of Tsallis entropy. An intuitive understanding of this result is discussed in relation to the nontrivial entangled structure exhibited by the quantum vacuum for mixed fields, combined with the Pauli exclusion principle.

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“…In describing complex systems, quantum algebra and quantum groups have been the subject of intensive research in several physical fields such as cosmic strings and black holes [11], conformal quantum mechanics [12], nuclear and high energy physics [13,14,15], fractional quantum Hall effect and high-T c superconductors [16]. From the seminal work of Biedenharn [17] and Macfarlane [18], it was clear that the q-calculus, originally introduced by Heine [19] and by Jackson [20] in the study of the basic hypergeometric series [21], plays a central role in the representation of the quantum groups with a deep physical meaning [22,23,24]. Furthermore, it is remarkable to observe that the q-calculus is very well suited for to describe fractal and multifractal systems.…”

Section: Introductionmentioning

confidence: 99%

Deformed Quantum Statistics in Two Dimensions

Lavagno

Swamy

2009

Int. J. Mod. Phys. B

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It is known from the early work of May in 1964 that ideal Bose gas do not exhibit condensation phenomenon in two dimensions. On the other hand, it is also known that the thermostatistics arising from q-deformed oscillator algebra has no connection with the spatial dimensions of the system. Our recent work concerns the study of important thermodynamic functions such as the entropy, occupation number, internal energy and specific heat in ordinary three spatial dimensions, where we established that such thermostatistics is developed by consistently replacing the ordinary thermodynamic derivatives by the Jackson derivatives. The thermostatistics of q-deformed bosons and fermions in two spatial dimensions is an unresolved question and that is the subject of this investigation. We study the principal thermodynamic functions of both bosons and fermions in the two dimensional q-deformed formalism and we find that, different from the standard case, the specific heat of q-boson and q-fermion ideal gas, at fixed temperature and number of particle, are no longer identical.

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122. [K. 20. f.] The Fundamental Formulae of Spherical Trigonometry.

Cited by 29 publications

References 0 publications

Generalized thermodynamics ofq-deformed bosons and fermions

Generalized thermodynamics ofq-deformed bosons and fermions

Nonextensive Tsallis statistics in Unruh effect for Dirac neutrinos

Deformed Quantum Statistics in Two Dimensions

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