Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9612190 · Journal of Physics Condensed Matter

The internal energy and condensate fraction of a trapped interacting Bose gas

Anna Minguzzi, S Conti, M P Tosi

Published Feb 3, 1997• 61 citations
arXivHTMLPDF

Abstract

We present a semiclassical two-fluid model for an interacting Bose gas confined in an anisotropic harmonic trap and solve it in the experimentally relevant region for a spin-polarized gas of atoms, obtaining the temperature dependence of the internal energy and of the condensate fraction. Our results are in agreement with recent experimental observations by Ensher et al .

DOI
10.1088/0953-8984/9/5/001

Related papers

Condensate fraction and critical temperature of a trapped interacting Bose gas

S. Giorgini, Лев П. Питаевский, S. Stringari

By using a mean-field approach, based on the Popov approximation, we calculate the temperature dependence of the condensate fraction of an interacting Bose gas of N atoms confined in an anisotropic harmonic trap. For systems interacting with repulsive forces we find a significant decrease of the condensate fraction and of the critical temperature with respect to the predictions of the noninteracting model with the same value of N. An analytic result for the shift of the critical temperature holding to first order in the scattering length is also derived. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9607117•Physical Review A•Dec 1, 1996•302 citations

Momentum distribution of an interacting Bose-Einstein condensed gas at finite temperature

Anna Minguzzi, Patrizia Vignolo, Mario P. Tosi

We use a semiclassical two-fluid model to study the momentum distribution of a Bose-Einstein condensed gas with repulsive interactions inside a harmonic trap at finite temperature, with specific focus on atomic hydrogen. We give particular attention to the average kinetic energy, which is almost entirely associated with the thermal cloud. A nonlinear dependence of the kinetic energy on temperature is displayed, affording a precise way to assess the temperature of the gas. We also show that the kinetic energy increases with the strength of the interactions, reflecting an enhanced rate of depletion of the condensate with increasing temperature.

arXiv:cond-mat/0003110•Physical Review A•Jul 17, 2000•10 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

Scaling and Thermodynamics of a Trapped Bose-Condensed Gas

S. Giorgini, Лев П. Питаевский, S. Stringari

We investigate the thermodynamics of a Bose gas interacting with repulsive forces and confined in a harmonic trap. We show that the relevant parameters of the system (temperature, number $N$ of atoms, harmonic oscillator length, deformation of the trap, $s$-wave scattering length) fix its thermodynamic behavior in the large $N$ limit through two dimensionless scaling parameters. These are the reduced temperature $t\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}T/{T}_{c}^{0}$ and the ratio $\ensuremath{\eta}$ between the $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ value of the chemical potential, evaluated in the Thomas-Fermi limit, and the critical temperature ${T}_{c}^{0}$ of the noninteracting model. The scaling functions relative to the condensate fraction, energy, chemical potential, and moment of inertia are calculated within the Popov approximation.

arXiv:cond-mat/9612192•Physical Review Letters•May 26, 1997•86 citations

Critical temperature of a Rashba spin-orbit-coupled Bose gas in a harmonic trap

Hui Hu, Xia-Ji Liu

We investigate theoretically Bose-Einstein condensation of an ideal, trapped Bose gas in the presence of Rashba spin-orbit coupling. Analytic results for the critical temperature and condensate fraction are derived based on a semiclassical approximation to the single-particle-energy spectrum and density of states and are compared with exact results obtained by explicitly summing discrete energy levels for a small number of particles. We find a significant decrease of the critical temperature and of the condensate fraction due to finite spin-orbit coupling. For a large coupling strength and a finite number of particles $N$, the critical temperature scales as ${N}^{2/5}$ and ${N}^{2/3}$ in three and two dimensions, respectively, contrasted to the predictions of ${N}^{1/3}$ and ${N}^{1/2}$ in the absence of spin-orbit coupling. Finite-size corrections in three dimensions are also discussed.

arXiv:1112.2799•Physical Review A•Jan 12, 2012•29 citations

Interaction Dependence Thermodynamical parameters of Harmonically Trapped Bose gas

Ahmed S. Hassan, Shemi S.M. Soliman, Emad H. Soliman

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.

arXiv:0909.4755•Sep 25, 2009•0 citations
We present a semiclassical two-fluid model for an interacting Bose gas confined in an anisotropic harmonic trap and solve it in the experimentally relevant region for a spin-polarized gas of atoms, obtaining the temperature dependence of the internal energy and of the condensate fraction. Our results are in agreement with recent experimental observations by Ensher et al .
By using a mean-field approach, based on the Popov approximation, we calculate the temperature dependence of the condensate fraction of an interacting Bose gas of N atoms confined in an anisotropic harmonic trap. For systems interacting with repulsive forces we find a significant decrease of the condensate fraction and of the critical temperature with respect to the predictions of the noninteracting model with the same value of N. An analytic result for the shift of the critical temperature holding to first order in the scattering length is also derived. \textcopyright{} 1996 The American Physical Society.
We use a semiclassical two-fluid model to study the momentum distribution of a Bose-Einstein condensed gas with repulsive interactions inside a harmonic trap at finite temperature, with specific focus on atomic hydrogen. We give particular attention to the average kinetic energy, which is almost entirely associated with the thermal cloud. A nonlinear dependence of the kinetic energy on temperature is displayed, affording a precise way to assess the temperature of the gas. We also show that the kinetic energy increases with the strength of the interactions, reflecting an enhanced rate of depletion of the condensate with increasing 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 investigate the thermodynamics of a Bose gas interacting with repulsive forces and confined in a harmonic trap. We show that the relevant parameters of the system (temperature, number NNN of atoms, harmonic oscillator length, deformation of the trap, sss-wave scattering length) fix its thermodynamic behavior in the large NNN limit through two dimensionless scaling parameters. These are the reduced temperature t=T/Tc0t\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}T/{T}_{c}^{0}t=T/Tc0​ and the ratio $\ensuremath{\eta}$ between the T=0T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0T=0 value of the chemical potential, evaluated in the Thomas-Fermi limit, and the critical temperature Tc0{T}_{c}^{0}Tc0​ of the noninteracting model. The scaling functions relative to the condensate fraction, energy, chemical potential, and moment of inertia are calculated within the Popov approximation.
We investigate theoretically Bose-Einstein condensation of an ideal, trapped Bose gas in the presence of Rashba spin-orbit coupling. Analytic results for the critical temperature and condensate fraction are derived based on a semiclassical approximation to the single-particle-energy spectrum and density of states and are compared with exact results obtained by explicitly summing discrete energy levels for a small number of particles. We find a significant decrease of the critical temperature and of the condensate fraction due to finite spin-orbit coupling. For a large coupling strength and a finite number of particles NNN, the critical temperature scales as N2/5{N}^{2/5}N2/5 and N2/3{N}^{2/3}N2/3 in three and two dimensions, respectively, contrasted to the predictions of N1/3{N}^{1/3}N1/3 and N1/2{N}^{1/2}N1/2 in the absence of spin-orbit coupling. Finite-size corrections in three dimensions are also discussed.
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.