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/0611490

Static Properties of Trapped Bose Gases at Finite Temperature: I. Thomas- Fermi Limit

Mohamed Benarous, Samet, H. Chachou

Published Nov 18, 2006• 0 citations
arXivHTMLPDF

Abstract

We rely on a variational approach to derive a set of equations governing a trapped self-interacting Bose gas at finite temperature. In this work, we analyze the static situation both at zero and finite temperature in the Thomas-Fermi limit. We derive simple analytic expressions for the condensate properties at finite temperature. The noncondensate and anomalous density profiles are also analyzed in terms of the condensate fraction. The results are quite encouraging owing to the simplicity of the formalism.

DOI
10.48550/arxiv.cond-mat/0611490

Related papers

Variational HFB Equations in the Thomas-Fermi Limit for Ultracold Trapped Gases

Mohamed Benarous

We derive variationally the HFB equations for a trapped self-interacting Bose gas at finite temperature. In the Thomas-Fermi limit, we obtain simple expressions for the condensate, the non condensate and the anomalous densities. Their behavior in terms of the condensate fraction meets qualitatively the experimental data. In particular, the non condensate and the anomalous densities are peaked at the center of the trap and not at the edges as predicted by the self-consistent HFB calculations.

arXiv:0803.1503•Mar 10, 2008•0 citations

Dynamical Variational Approach for Trapped Gases at Finite Temperature

Mohamed Benarous

We analyze the static TDHFB equations in the Thomas-Fermi limit for a gas of bosons in a harmonic trap . These equations naturally generalize the Gross-Pitaevskii equation. We first build a simple enough method that allows f or the determination of the various density profile s. At zero temperature, we obtain familiar expressions for the chemical pot ential and the condensate radius. The standard Thomas-Fermi profile for the condensate density is also recovered. For finit e temperatures and above the transition, we derive analytical expressions for the condensate radius, the chemical potential, the number of condensed atoms and the depletion as functions of the temperature. We observe that the condensate radius and the column density are surprisingly very slow f unctions of the temperature. Furthermore, the non-condensed density, although being quite uniform inside the trap, gro ws rapidly with the temperature. These facts imply therefore that the c ondensed atoms are very strongly attached and exhib it a certain robustness against ''decondensation''. Moreover, the transitio n to the non condensed phase seems to be much more controlled by the thermal cloud which rapidly grows from the borders toward the centre of the trap.

Revue Nature et Technologie•Jun 30, 2011•0 citations

FINITE TEMPERATURE THOMAS-FERMI LIMIT FOR ULTRACOLD TRAPPED GASES

Mohamed Benarous

The HFB equations for a trapped Bose gas are revisite d. In the Thomas-Fermi limit, we derive tractable e xpressions for condensate, non condensate and anomalous densities. Their behaviour in terms of condensate fractions a grees with the experimental data qualitatively. In particular, non condensate and anomalous densities are peaked at t he centre of the trap and not at the edges, as predicted by the self-cons istent HFB calculations.

The African review of physics•Dec 2, 2010•0 citations

Variational Thomas-Fermi theory of a nonuniform Bose condensate at zero temperature

Eddy Timmermans, Paolo Tommasini, Kerson Huang

We derive a description of the spatially inhomogeneous Bose-Einstein condensate, treating the system locally as a homogeneous Bose gas. This approach, similar to the Thomas-Fermi model for the inhomogeneous many-particle fermion system, is well suited to describe the atomic Bose-Einstein condensates that have recently been obtained experimentally through atomic trapping and cooling. In this paper, we confine our attention to the zero-temperature case, although the treatment can be generalized to finite temperatures, as we shall discuss elsewhere. Several features of this approach, which we shall call the Thomas-Fermi-Bogoliubov description, are very attractive. (i) It is simpler than the Hartree-Fock-Bogoliubov technique. We can obtain analytical results in the case of weakly interacting bosons for quantities such as the chemical potential, the local depletion, pairing, pressure, and density of states. (ii) The method provides an estimate for the error due to the inhomogeneity of the Bose-condensed system. This error is a local quantity so that the validity of the description for a given trap and a given number of trapped atoms can be tested as a function of position. We see, for example, that at the edge of the condensate the Thomas-Fermi-Bogoliubov theory always breaks down. (iii) The Thomas-Fermi-Bogoliubov description can be generalized to treat the statistical mechanics of the Bose gas at finite temperatures.

arXiv:cond-mat/9609234•Physical Review A•May 1, 1997•74 citations

Finite Temperature Excitations of a Trapped Bose Gas

David A. W. Hutchinson, E. Zaremba, Adam Griffin

We present a detailed study of the temperature dependence of the condensate and noncondensate density profiles of a Bose-condensed gas in a parabolic trap. These quantities are calculated self-consistently using the Hartree-Fock-Bogoliubov equations within the Popov approximation. Below the Bose-Einstein transition the excitation frequencies have a relatively weak temperature dependence even though the condensate is strongly depleted. As the condensate density goes to zero through the transition, the excitation frequencies are strongly affected and approach the frequencies of a noninteracting trapped gas in the high temperature limit.

arXiv:cond-mat/9611023•Physical Review Letters•Mar 10, 1997•262 citations

Zero-temperature properties of a trapped Bose-condensed gas: Beyond the Thomas-Fermi approximation

Emil Lundh, C. J. Pethick, H. Smith

We consider the leading corrections to the Thomas-Fermi approach to the description of the properties of a magnetically trapped, Bose-condensed cloud of atoms. Simple analytical expressions are derived for the kinetic energy in terms of an effective cutoff length, which we calculate numerically by considering the one-dimensional problem for a linear-ramp potential. We also determine the lowest angular velocity at which it is energetically favorable for a vortex to enter the cloud. For large clouds, our results are in excellent agreement with available numerical calculations.

Physical Review A•Mar 1, 1997•152 citations
We rely on a variational approach to derive a set of equations governing a trapped self-interacting Bose gas at finite temperature. In this work, we analyze the static situation both at zero and finite temperature in the Thomas-Fermi limit. We derive simple analytic expressions for the condensate properties at finite temperature. The noncondensate and anomalous density profiles are also analyzed in terms of the condensate fraction. The results are quite encouraging owing to the simplicity of the formalism.
We analyze the static TDHFB equations in the Thomas-Fermi limit for a gas of bosons in a harmonic trap . These equations naturally generalize the Gross-Pitaevskii equation. We first build a simple enough method that allows f or the determination of the various density profile s. At zero temperature, we obtain familiar expressions for the chemical pot ential and the condensate radius. The standard Thomas-Fermi profile for the condensate density is also recovered. For finit e temperatures and above the transition, we derive analytical expressions for the condensate radius, the chemical potential, the number of condensed atoms and the depletion as functions of the temperature. We observe that the condensate radius and the column density are surprisingly very slow f unctions of the temperature. Furthermore, the non-condensed density, although being quite uniform inside the trap, gro ws rapidly with the temperature. These facts imply therefore that the c ondensed atoms are very strongly attached and exhib it a certain robustness against ''decondensation''. Moreover, the transitio n to the non condensed phase seems to be much more controlled by the thermal cloud which rapidly grows from the borders toward the centre of the trap.
We derive a description of the spatially inhomogeneous Bose-Einstein condensate, treating the system locally as a homogeneous Bose gas. This approach, similar to the Thomas-Fermi model for the inhomogeneous many-particle fermion system, is well suited to describe the atomic Bose-Einstein condensates that have recently been obtained experimentally through atomic trapping and cooling. In this paper, we confine our attention to the zero-temperature case, although the treatment can be generalized to finite temperatures, as we shall discuss elsewhere. Several features of this approach, which we shall call the Thomas-Fermi-Bogoliubov description, are very attractive. (i) It is simpler than the Hartree-Fock-Bogoliubov technique. We can obtain analytical results in the case of weakly interacting bosons for quantities such as the chemical potential, the local depletion, pairing, pressure, and density of states. (ii) The method provides an estimate for the error due to the inhomogeneity of the Bose-condensed system. This error is a local quantity so that the validity of the description for a given trap and a given number of trapped atoms can be tested as a function of position. We see, for example, that at the edge of the condensate the Thomas-Fermi-Bogoliubov theory always breaks down. (iii) The Thomas-Fermi-Bogoliubov description can be generalized to treat the statistical mechanics of the Bose gas at finite temperatures.
We present a detailed study of the temperature dependence of the condensate and noncondensate density profiles of a Bose-condensed gas in a parabolic trap. These quantities are calculated self-consistently using the Hartree-Fock-Bogoliubov equations within the Popov approximation. Below the Bose-Einstein transition the excitation frequencies have a relatively weak temperature dependence even though the condensate is strongly depleted. As the condensate density goes to zero through the transition, the excitation frequencies are strongly affected and approach the frequencies of a noninteracting trapped gas in the high temperature limit.
We consider the leading corrections to the Thomas-Fermi approach to the description of the properties of a magnetically trapped, Bose-condensed cloud of atoms. Simple analytical expressions are derived for the kinetic energy in terms of an effective cutoff length, which we calculate numerically by considering the one-dimensional problem for a linear-ramp potential. We also determine the lowest angular velocity at which it is energetically favorable for a vortex to enter the cloud. For large clouds, our results are in excellent agreement with available numerical calculations.