Finite temperature analytical results for a harmonically confined gas obeying exclusion statistics in<i>d</i>-dimensions

MacDonald, Zachary; Zyl, Brandon P. van

doi:10.1088/1751-8113/46/4/045001

Cited by 5 publications

(4 citation statements)

References 36 publications

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“…[1] and the statistical mechanics of FES systems was formulated by several authors, employing different methods [2][3][4][5][6][7][8]. The FES have been applied to the description of several types of interacting particle systems [1][2][3][4][5][6][7][9][10][11][12] and the properties of FES systems in different numbers of dimensions and trapping potentials have been studied [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. A general method for the description of Fermi liquid type of systems as ideal FES gases have been proposed in Ref.…”

Section: Introductionmentioning

confidence: 99%

From fractional exclusion statistics back to Bose and Fermi distributions

Anghel¹

2013

Physics Letters A

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Fractional exclusion statistics (FES) is a generalization of the Bose and Fermi statistics. Typically, systems of interacting particles are described as ideal FES systems and the properties of the FES systems are calculated from the properties of the interacting systems. In this paper I reverse the process and I show that a FES system may be described in general as a gas of quasiparticles which obey Bose or Fermi distributions; the energies of the newly defined quasiparticles are calculated starting from the FES equations for the equilibrium particle distribution. In the end I use a system in the effective mass approximation as an example to show how the procedure works.

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Section: Introductionmentioning

confidence: 99%

From fractional exclusion statistics back to Bose and Fermi distributions

Anghel¹

2013

Physics Letters A

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“…In addition to that, they show that one can obtain Bose-Einstein distribution f BE , from Gentile distribution f G , in thermodynamic limit when one takes two limits, maximum occupation number q → ∞, and the total number of particles (N → ∞) in a given order (f BE ≡ lim <N >→∞ lim n→∞ f G ) [15]. Furthermore, Donald and Zly derived thermodynamic properties for a harmonically confined gas obeying Gentile statistics in d-dimensions and compared these results with a similar system obeying Haldene-Wu statistics [16].…”

Section: Introductionmentioning

confidence: 99%

A new method for derivation of statistical weight of the Gentile Statistics

Selvi

Uncu

2015

Physica A: Statistical Mechanics and its Applications

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h i g h l i g h t s• We obtain statistical weight of Gentile distribution (GD) using inductive method. • We calculate the statistical weight for various intermediate particles obeying GD.• The inductive method needs less computer time compared to previous methods. a b s t r a c tWe present a new method for obtaining the statistical weight of the Gentile Statistics. In a recent paper, Perez and Tun presented an approximate combinatoric and an exact recursive formula for the statistical weight of Gentile Statistics, beginning from bosonic and fermionic cases, respectively Hernandez-Perez and Tun (2007). In this paper, we obtain two exact, one combinatoric and one recursive, formulae for the statistical weight of Gentile Statistics, by another approach. The combinatoric formula is valid only for special cases, whereas recursive formula is valid for all possible cases. Moreover, for a given qmaximum number of particles that can occupy a level for Gentile statistics-the recursive formula we have derived gives the result much faster than the recursive formula presented in Hernandez-Perez and Tun (2007), when one uses a computer program. Moreover we obtained the statistical weight for the distribution proposed by .

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“…A stochastic method for the simulation of the time evolution of FES systems was introduced in Ref. [26] as a generalization of a similar method used for Bose and Fermi systems [27], whereas the relatively recent experimental realization of the Fermi degeneracy in cold atomic gases has renewed the interest in the theoretical investigation of non-ideal Fermi systems at low temperatures and their interpretation as ideal FES systems [23,[28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Equivalence between fractional exclusion statistics and self-consistent mean-field theory in interacting-particle systems in any number of dimensions

2013

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We describe a mean field interacting particle system in any number of dimensions and in a generic external potential as an ideal gas with fractional exclusion statistics (FES). We define the FES quasiparticle energies, we calculate the FES parameters of the system and we deduce the equations for the equilibrium particle populations. The FES gas is "ideal," in the sense that the quasiparticle energies do not depend on the other quasiparticle levels populations and the sum of the quasiparticle energies is equal to the total energy of the system. We prove that the FES formalism is equivalent to the semi-classical or Thomas Fermi limit of the self-consistent mean-field theory and the FES quasiparticle populations may be calculated from the Landau quasiparticle populations by making the correspondence between the FES and the Landau quasiparticle energies. The FES provides a natural semi-classical ideal gas description of the interacting particle gas.

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Finite temperature analytical results for a harmonically confined gas obeying exclusion statistics ind-dimensions

Cited by 5 publications

References 36 publications

From fractional exclusion statistics back to Bose and Fermi distributions

From fractional exclusion statistics back to Bose and Fermi distributions

A new method for derivation of statistical weight of the Gentile Statistics

Equivalence between fractional exclusion statistics and self-consistent mean-field theory in interacting-particle systems in any number of dimensions

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