Thermodynamics of a trapped Bose-condensed gas

Giorgini, S.; Pitaevskiĭ, Lev P.; Stringari, S.

doi:10.1007/bf02396737

Cited by 34 publications

(47 citation statements)

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“…The same kind of semiclassical results have also been obtained in Ref. [13] for a trapped Bose gas using the Popov approximation (which corresponds to the HFB withm=0). Since the local quasiparticle energy E p (R) given by (60) depends on the normal and anomalous densities, the quantities in (60), (64) and (65) must be solved self-consistently, as in Ref.…”

Section: Static Hfb Equilibrium Solutions In the Semi-classical Asupporting

confidence: 76%

“…The only region where the TF approximation for the order parameter is inadequate is close to the classical turning points at the condensate boundary [13,15], which is consistent with inapplicability of the semi-classical approximation near these points.…”

Section: Static Hfb Equilibrium Solutions In the Semi-classical Amentioning

confidence: 73%

“…Therefore, we can assume that u i (R) and v i (R) have a form of a plane waves with a slowly varying amplitude in that region [13], i.e.…”

Section: Static Hfb Equilibrium Solutions In the Semi-classical Amentioning

confidence: 99%

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Coupled Hartree-Fock-Bogoliubov kinetic equations for a trapped Bose gas

Imamovic-Tomasovic

Griffin

1999

Phys. Rev. A

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Using the Kadanoff-Baym non-equilibrium Green's function formalism, we derive the self-consistent Hartree-Fock-Bogoliubov (HFB) collisionless kinetic equations and the associated equation of motion for the condensate wavefunction for a trapped Bose-condensed gas. Our work generalizes earlier work by Kane and Kadanoff (KK) for a uniform Bose gas. We include the off-diagonal (anomalous) pair correlations, and thus we have to introduce an off-diagonal distribution function in addition to the normal (diagonal) distribution function. This results in two coupled kinetic equations. If the off-diagonal distribution function can be neglected as a higher-order contribution, we obtain the semi-classical kinetic equation recently used by Zaremba, Griffin and Nikuni (based on the simpler Popov approximation). We discuss the static local equilibrium solution of our coupled HFB kinetic equations within the semiclassical approximation. We also verify that a solution is the rigid in-phase oscillation of the equilibrium condensate and non-condensate density profiles, oscillating with the trap frequency.

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Section: Static Hfb Equilibrium Solutions In the Semi-classical Asupporting

confidence: 76%

Section: Static Hfb Equilibrium Solutions In the Semi-classical Amentioning

confidence: 73%

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Coupled Hartree-Fock-Bogoliubov kinetic equations for a trapped Bose gas

Imamovic-Tomasovic

Griffin

1999

Phys. Rev. A

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“…The time-independent problem, corresponding to finding initial conditions of our simulations, can be solved by propagating in imaginary time, so that an arbitrary wavefunction quickly diffuses to the ground state solution. The equilibrium thermal distribution can be calculated under a semi-classical approximation [19], where in a harmonic trap of mean frequencyω the discrete energy levels are replaced by a continuous function…”

mentioning

confidence: 99%

Damping and revivals of collective oscillations in a finite-temperature model of trapped Bose-Einstein condensation

Jackson

Adams

2001

Phys. Rev. A

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We utilize a two-gas model to simulate collective oscillations of a Bose-Einstein condensate at finite temperatures. The condensate is described using a generalized GrossPitaevskii equation, which is coupled to a thermal cloud modelled by a Monte Carlo algorithm. This allows us to include the collective dynamics of both the condensed and non-condensed components self-consistently. We simulate quadrupolar excitations, and measure the damping rate and frequency as a function of temperature. We also observe revivals in condensate oscillations at high temperatures, and in the thermal cloud at low temperature. Extensions of the model to include non-equilibrium effects and describe more complex phenomena are discussed.PACS numbers: 03.75. Fi, 05.30.Jp, 67.40.Db The first experimental observation of Bose-Einstein condensation (BEC) in magnetically trapped alkali atoms in 1995 [1-3] was a precursor to an explosion of interest in the properties of weakly-interacting Bose gases. Much of the subsequent theory [4] has focused on the dynamics of the condensate, including phenomena such as collective excitations and vortex motion. In the limit of zero temperature, one can represent the condensate by a macroscopic wavefunction analogous to a classical field. In this case the behavior can be described in terms of the GrossPitaevskii (GP) equation, which has the form of a nonlinear Shrödinger equation. Extension of the description to finite temperatures, where one must include fluctuations upon the condensate wavefunction, is a considerable challenge. However, the motivation is clear, as such a description would allow direct comparison with experiments where a non-condensed thermal cloud is present, as well as revealing new phenomena such as damping of collective modes [5][6][7][8][9][10] and the decay of metastable vortices [11,12].Amongst the most compelling evidence for the validity of the GP equation at low temperatures is its quantitative agreement with experiment for low-energy collective modes. However, consistent theoretical descriptions at higher temperatures have proved far more elusive, where experiments have demonstrated marked frequency shifts and damping of the condensate modes in the presence of a significant non-condensed component [9,10]. Theoretical studies have tended to concentrate on one of two regimes, depending upon the density and temperature of the system. At high densities, where collisions are sufficiently rapid to force the system into local equilibrium, the dynamics of the condensate and thermal cloud can be described by a set of coupled hydrodynamical equations [13][14][15]. Damping mechanisms in this case are of a dissipative type (i.e. viscosity and thermal relaxation). For very dilute systems or at low temperatures the mean free path of the elementary excitations become comparable to the size of the system and collisions play only a minor role. Damping in this collisionless regime is not related to thermalization processes but to coupling between excitations, and can be described within the fr...

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“…However, the quantum statistical mechanics of the interacting system remain unsolvable and one has to resort to approximated schemes. In this respect, the semiclassical Hartree-Fock (HF) approximation [9] provides the scheme mostly used for taking into account the interatomic interactions [10]. This mean-field theory avoids the difficulty of solving the full many-body Schrödinger equation for an interacting system by reducing the many-body problem to a one-body problem via the introduction of an appropriate mean field potential generated by all the other particles.…”

Section: Introductionmentioning

confidence: 99%