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Thomas-Fermi approximation to static vortex states in superfluid trapped atomic gases

Michael Urban, Peter Schuck, X. Vi�as

arXiv:cond-mat/0207261The European Physical Journal DNov 1, 20032 citations

Dynamics of Trapped Bose Gases at Finite Temperatures

E. Zaremba, Tetsuro Nikuni, Adam Griffin

arXiv:cond-mat/9903029Journal of Low Temperature PhysicsAug 1, 1999312 citations

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

Mohamed Benarous, Samet, H. Chachou

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 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.

arXiv:cond-mat/0611490Nov 18, 20060 citations

On the dynamics of finite temperature trapped Bose gases

Avy Soffer, Minh-Binh Tran

arXiv:1609.07686Advances in MathematicsDec 13, 201728 citations

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:0803.1503Mar 10, 20080 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.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 TechnologieJun 30, 20110 citations

Static properties of trapped bose gases at finite temperature: Thomas-Fermi limit

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