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arXiv:1401.4029 · Physical Review A

Weakly nonadditive Polychronakos statistics

Andrij A. Rovenchak

Published May 16, 2014• 15 citations
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Abstract

A two-parameter fractional statistics is proposed, which can be used to model a weakly interacting Bose system. It is shown that the parameters of the introduced weakly nonadditive Polychronakos statistics can be linked to the effects of interactions as well as to finite-size corrections. Calculations are made of the specific heat and condensate fraction of the model system corresponding to harmonically trapped Rb-87 atoms. The behavior of the specific heat of three-dimensional isotropic harmonic oscillators with respect tothe statistics parameters is studied in the temperature domain including the BEC-like phase-transition point.

DOI
10.1103/physreva.89.052116

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A two-parameter fractional statistics is proposed, which can be used to model a weakly interacting Bose system. It is shown that the parameters of the introduced weakly nonadditive Polychronakos statistics can be linked to the effects of interactions as well as to finite-size corrections. Calculations are made of the specific heat and condensate fraction of the model system corresponding to harmonically trapped Rb-87 atoms. The behavior of the specific heat of three-dimensional isotropic harmonic oscillators with respect tothe statistics parameters is studied in the temperature domain including the BEC-like phase-transition point.
A two-parametric fractional statistics is proposed, which can be used to model a weakly-interacting Bose-system. It is shown that the parameters of the introduced weakly-nonextensive Polychronakos statistics can be linked to effects of interactions as well as finite-size corrections. The calculations of the specific heat and condensate frac-tion of the model system corresponding to harmonically trapped Rb-87 atoms are made. The behavior of the specific heat of three-dimensional isotropic harmonic oscillators with respect to the values of the statis-tics parameters is studied in the temperature domain including the BEC-like phase transition point. 1
The thermodynamic properties and finite-size scaling of weakly interacting Bose gases with a finite number of particles confined in a cubic box of volume L3{L}^{3}L3 with periodic boundary conditions are investigated theoretically based on an exact recursion relation for the canonical-ensemble partition function. In a similar manner to the case of an ideal Bose gas, the recursive scheme of the interacting finite system at any temperatures is established in the framework of the Bogoliubov theory. The temperature dependence of the condensate fraction and specific heat with different particles and interactions is obtained numerically. By defining two different transition temperatures of the finite systems, the effect of interactions on the transition temperatures yields the different and nonmonotonous behaviors. The finite-size scaling condensate fraction at the transition temperature for the systems is also discussed. It is shown that the calculated finite-size scaling is universally independent on the various system sizes and transition temperatures.
In this paper the thermodynamical parameters of a condensed Boson gas are calculated from the partial derivative of the grand potential. In particular, the analytical expressions for some important parameters, such as the condensed fraction, specific heat, critical temperature, effective size, and release energy are investigated. The mean effects which can be altered the ideal Bose gas, such as finite size, highly anisotropic of the external potential and interatomic interaction effects are considered simultaneously. Some new characteristics of the trapped interacting Bose gases in a highly anisotropic trap are revealed. The calculated result for the condensed fraction is compared with the ongoing Stuttgart experiment for 52Cr (Griesmaier et al., Phys. Rev. Lett. 94, 160401(2005)) directly. Good agreement between both the theoretical and experimental data are obtained.
We study the thermodynamic behavior of an ideal gas of bosons trapped in a three-dimensional anisotropic harmonic-oscillator potential. The condensate fraction as well as the specific heat is calculated using the Euler-Maclaurin approximation. For a finite number of particles there is no phase transition, but there is a well-defined temperature at which the condensation starts. We also consider condensation in lower dimensions, and, for one-dimensional systems, we discuss the dependence of the condensate fraction and heat capacity on the ensemble used.
We show various aspects of finite size effects on Bose-Einstein condensation(BEC). In the first section we introduce very briefly the BEC of harmonically trapped ideal Bose gas. In the second section we theoretically argued that Bose-Einstein(B-E) statistics needs a correction for finite system at ultralow temperatures. As a corrected statistics we introduced a Tsallis type of generalized B-E statistics. The condensate fraction calculated with this generalized B-E statistics, is satisfied well with the experimental result. In the third section we show how to apply the scaling theory in an inhomogeneous system like harmonically trapped Bose condensate at finite temperatures. We calculate the temperature dependence of the critical number of particles by a scaling theory within the Hartree-Fock approximation and find that there is a dramatic increase in the critical number of particles as the condensation point is approached. Our results support the experimental result which was obtained well below the condensation temperature. In the fourth section we concentrate on the thermodynamic Casimir force on the Bose-Einstein condensate. We explored the temperature dependence of the Casimir force.