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BEC in Nonextensive Statistical Mechanics

Luca Salasnich

Published Jan 1, 1999• 9 citations
OpenAlex

Abstract

We discuss the Bose-Einstein condensation (BEC) for an ideal gas of bosons in the framework of Tsallis’s nonextensive statistical mechanics. We study the corrections to the standard BEC formulas due to a weak nonextensivity of the system. In particular, we consider three cases in the D-dimensional space: the homogeneous gas, the gas in a harmonic trap and the relativistic homogenous gas. The results show that small deviations from the extensive Bose statistics produce remarkably large changes in the BEC transition temperature. PACS numbers: 05.30-d; 03.75.Fi 1 A decade ago, Tsallis introduced a nonextensive statistical mechanics (NSM) to describe systems for which the additivity property of entropy does not hold. 1 The NSM can describe systems for which long-range microscopic memory, fractal space-time constraints or long-range interactions affect the thermalization process. 2 The NSM is characterized by a parameter q such

Related papers

BEC in Nonextensive Statistical Mechanics: Some Additional Results

Luca Salasnich

In a recent paper [Int. J. Mod. Phys. B 14, 405 (2000)] we discussed the Bose-Einstein condensation (BEC) in the framework of Tsallis’s nonextensive statistical mechanics. In particular, we studied an ideal gas of bosons in a confining harmonic potential. In this memoir we generalize our previous analysis by investigating an ideal Bose gas in a generic power-law external potential. We derive analytical formulas for the energy of the system, the BEC transition temperature and the condensed fraction. PACS numbers: 05.30-d; 03.75.Fi 1 Recently we analyzed the consequences of weak nonextensivity on Bose-Einstein Condensation for an ideal Bose gas 1 by using Tsallis’s nonextensive statistical mechanics (NSM). 2 From the nonextensive Bose-Einstein distribution 3−5 we derived the BEC transition temperature, the condensed fraction and the energy per particle in three different cases: the homogeneous gas, the gas in a harmonic trap and the relativistic homogenous gas. In this short contribution we generalize our previous results by considering the ideal Bose gas in a generic power-law potential. All the calculations are performed by assuming a D-dimensional space. The NSM predicts that, for an ideal quantum gas of identical bosons in the grand canonical ensemble, the weak nonextensivity formula of the average number of particles with energy ǫ is given by 〈n(ǫ)〉q = 1

•Jan 1, 2001•7 citations

BEC IN NONEXTENSIVE STATISTICAL MECHANICS

LUCA SALASNICH

We discuss the Bose–Einstein condensation (BEC) for an ideal gas of bosons in the framework of Tsallis's nonextensive statistical mechanics. We study the corrections to the st and ard BEC formulas due to a weak nonextensivity of the system. In particular, we consider three cases in the D-dimensional space: the homogeneous gas, the gas in a harmonic trap and the relativistic homogenous gas. The results show that small deviations from the extensive Bose statistics produce remarkably large changes in the BEC transition temperature.

arXiv:cond-mat/9911453•International Journal of Modern Physics B•Feb 10, 2000•9 citations

BEC IN NONEXTENSIVE STATISTICAL MECHANICS: SOME ADDITIONAL RESULTS

LUCA SALASNICH

In a recent paper1 we discussed the Bose–Einstein condensation (BEC) in the framework of Tsallis's nonextensive statistical mechanics. In particular, we studied an ideal gas of bosons in a confining harmonic potential. In this memoir we generalize our previous analysis by investigating an ideal Bose gas in a generic power-law external potential. We derive analytical formulas for the energy of the system, the BEC transition temperature and the condensed fraction.

arXiv:cond-mat/0101350•International Journal of Modern Physics B•Apr 10, 2001•7 citations

Note on BEC in Nonextensive Statistical Mechanics

Kwok Sau Fa, Ervin Kaminski Lenzi

The generalized Bose-Einstein distribution, within the dilute gas assumption, in the nonextensive Tsallis statistics is worked without approximation for the Bose-Einstein condensation (BEC). The results obtained are compared with the recent results presented in Int. J. Mod. Phys. B 14, 405 (2000) by L. Salasnich. Furthermore, in order to promote a complete analysis for the BEC in the nonextensive scenario we also find exact expression within the normalized constraints in a harmonic trap.

Brazilian Journal of Physics•Jun 1, 2001•9 citations

Trapped interacting Bose gas in nonextensive statistical mechanics

B. Tanatar

We study the Bose-Einstein condensation (BEC) phenomenon in an interacting trapped Bose gas using the semiclassical two-fluid model and nonextensive statistical mechanics. The effects of nonextensivity characterized by a parameter are explored by calculating the temperature dependent thermodynamic properties, fraction of condensed particles, and density distributions of condensed and thermal components of the system. It is found that nonextensivity in the underlying statistical mechanics may have large effects on the BEC transition temperature.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Mar 18, 2002•11 citations

Finite Size Effect on Bose-Einstein Condensation

Shyamal Biswas

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.

arXiv:cond-mat/0606029•Jun 1, 2006•2 citations
We discuss the Bose-Einstein condensation (BEC) for an ideal gas of bosons in the framework of Tsallis’s nonextensive statistical mechanics. We study the corrections to the standard BEC formulas due to a weak nonextensivity of the system. In particular, we consider three cases in the D-dimensional space: the homogeneous gas, the gas in a harmonic trap and the relativistic homogenous gas. The results show that small deviations from the extensive Bose statistics produce remarkably large changes in the BEC transition temperature. PACS numbers: 05.30-d; 03.75.Fi 1 A decade ago, Tsallis introduced a nonextensive statistical mechanics (NSM) to describe systems for which the additivity property of entropy does not hold. 1 The NSM can describe systems for which long-range microscopic memory, fractal space-time constraints or long-range interactions affect the thermalization process. 2 The NSM is characterized by a parameter q such
In a recent paper [Int. J. Mod. Phys. B 14, 405 (2000)] we discussed the Bose-Einstein condensation (BEC) in the framework of Tsallis’s nonextensive statistical mechanics. In particular, we studied an ideal gas of bosons in a confining harmonic potential. In this memoir we generalize our previous analysis by investigating an ideal Bose gas in a generic power-law external potential. We derive analytical formulas for the energy of the system, the BEC transition temperature and the condensed fraction. PACS numbers: 05.30-d; 03.75.Fi 1 Recently we analyzed the consequences of weak nonextensivity on Bose-Einstein Condensation for an ideal Bose gas 1 by using Tsallis’s nonextensive statistical mechanics (NSM). 2 From the nonextensive Bose-Einstein distribution 3−5 we derived the BEC transition temperature, the condensed fraction and the energy per particle in three different cases: the homogeneous gas, the gas in a harmonic trap and the relativistic homogenous gas. In this short contribution we generalize our previous results by considering the ideal Bose gas in a generic power-law potential. All the calculations are performed by assuming a D-dimensional space. The NSM predicts that, for an ideal quantum gas of identical bosons in the grand canonical ensemble, the weak nonextensivity formula of the average number of particles with energy ǫ is given by 〈n(ǫ)〉q = 1
We discuss the Bose–Einstein condensation (BEC) for an ideal gas of bosons in the framework of Tsallis's nonextensive statistical mechanics. We study the corrections to the st and ard BEC formulas due to a weak nonextensivity of the system. In particular, we consider three cases in the D-dimensional space: the homogeneous gas, the gas in a harmonic trap and the relativistic homogenous gas. The results show that small deviations from the extensive Bose statistics produce remarkably large changes in the BEC transition temperature.
We study the Bose-Einstein condensation (BEC) phenomenon in an interacting trapped Bose gas using the semiclassical two-fluid model and nonextensive statistical mechanics. The effects of nonextensivity characterized by a parameter are explored by calculating the temperature dependent thermodynamic properties, fraction of condensed particles, and density distributions of condensed and thermal components of the system. It is found that nonextensivity in the underlying statistical mechanics may have large effects on the BEC transition temperature.
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.