Quantum gases and polylogs

Lee, M. Howard; Kim, Jangil

doi:10.1016/s0378-4371(01)00552-0

Cited by 14 publications

(2 citation statements)

References 14 publications

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“…Indeed, since the pioneering paper of Lee (1995), the polylogarithms have unified the statistical mechanics of ideal gases (cf. also Lee & Kim 2002 and the references therein). More recently, Ciccariello (2004) has noted that the unified description given by Lee (1995) can be obtained from Lerch's function, which generalizes the polylogarithm function (for details on Lerch's function see Erdélyi (1953), §1.11, pp.…”

Section: Introductionmentioning

confidence: 92%

On a connection between the polylogarithm function and the Bass diffusion model

Jodrá

2008

Proc. R. Soc. A.

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The purpose of this paper is to establish a connection between the polylogarithm function and a continuous probability distribution. We provide closed-form expressions in terms of the polylogarithm function for all the moments of a continuous random variable related to the Bass diffusion model, which was introduced by Bass and is widely used in marketing science. In addition, a new integral representation of the polylogarithm of order n is achieved from a probabilistic formulation.

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Section: Introductionmentioning

confidence: 92%

On a connection between the polylogarithm function and the Bass diffusion model

Jodrá

2008

Proc. R. Soc. A.

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“…In [2], it was observed that Newton's identity (4) corresponds to Landsberg's identity in physics [28], and equation ( 11) is related to a Bose-Fermi symmetry. Some specific examples for the mentioned Bose-Fermi symmetry can be found in [29][30][31].…”

Section: Partition Functionsmentioning

confidence: 99%

Applications of Supersymmetric Polynomials in Statistical Quantum Physics

Chernega,

Martsinkiv,

Vasylyshyn

et al. 2023

Quantum Reports

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We propose a correspondence between the partition functions of ideal gases consisting of both bosons and fermions and the algebraic bases of supersymmetric polynomials on the Banach space of absolutely summable two-sided sequences ℓ1(Z0). Such an approach allows us to interpret some of the combinatorial identities for supersymmetric polynomials from a physical point of view. We consider a relation of equivalence for ℓ1(Z0), induced by the supersymmetric polynomials, and the semi-ring algebraic structures on the quotient set with respect to this relation. The quotient set is a natural model for the set of energy levels of a quantum system. We introduce two different topological semi-ring structures into this set and discuss their possible physical interpretations.

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Polypseudologarithms revisited

Cvijović

2010

Physica A: Statistical Mechanics and its Applications

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Lee, in a series of papers, described a unified formulation of the statistical thermodynamics of ideal quantum gases in terms of the polylogarithm functions, $\textup{Li}_{s} (z)$. It is aimed here to investigate the functions $\textup{Li}_{s} (z),$ for $s = 0, -1, -2, ...,$ which are, following Lee, referred to as the polypseudologarithms (or polypseudologs) of order $n$. Various known results regarding polypseudologs, mainly obtained in widely differing contexts and currently scattered throughout the literature, have been brought together along with many new results and insights and they all have been proved in a simple and unified manner. In addition, a new general explicit closed-form formula for these functions involving the Carlitz--Scoville higher tangent numbers has been established.Comment: 10 page

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Quantum gases and polylogs

Cited by 14 publications

References 14 publications

On a connection between the polylogarithm function and the Bass diffusion model

On a connection between the polylogarithm function and the Bass diffusion model

Applications of Supersymmetric Polynomials in Statistical Quantum Physics

Polypseudologarithms revisited

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