BEC from a time-dependent variational point of view

Benarous, M.

doi:10.1016/j.aop.2005.05.006

Cited by 6 publications

(17 citation statements)

References 26 publications

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“…These results have also been obtained by many other authors, see e.g. [8,11,12]. Hence, one may safely approximate (2.10) by…”

Section: )supporting

confidence: 85%

“…A major well-known drawback of these methods is that they cannot be easily extended to situations where their main assumptions fail. In a previous paper [12], we rely on a different approach, based on the time-dependent variational principle of Balian and Vénéroni [13] , which allows one to overcome some of those restrictions. We obtained a set of three coupled dynamical equations, which we called "Time-Dependent Hartree-Fock-Bogoliubov" (TDHFB) equations, governing the evolution of Φ,ñ andm.…”

Section: Introductionmentioning

confidence: 99%

“…The paper is organized as follows. In section 2, we recall the main steps that have been used in [12] to derive the TDHFB equations. Then, we present the static solutions and discuss their properties at zero temperature.…”

Section: Introductionmentioning

confidence: 99%

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

Benarous

Chachou-Samet

2008

Eur. Phys. J. D

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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.

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“…These results have also been obtained by many other authors, see e.g. [8,11,12]. Hence, one may safely approximate (2.10) by…”

Section: )supporting

confidence: 85%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Benarous

Chachou-Samet

2008

Eur. Phys. J. D

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“…As one can immediately see, if T << T BEC , the zero temperature density profile can give an excellent description of the condensate in thermodynamic equilibrium with a thermal cloud. The effect of the presence of the thermal cloud results in the modification of the central density of the system [25], which consists now from the sum of the central density of the condensate and of the thermal cloud. However, in order to see if the approximation of the zero temperature indeed works, one have to estimate the temperature at which the Bose-Einstein condensation took place, and the corresponding density of the Universe.…”

Section: Discussion and Final Remarksmentioning

confidence: 99%

Finite temperature effects in Bose-Einstein condensed dark matter halos

Harkó

Madarassy

2012

J. Cosmol. Astropart. Phys.

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Once the critical temperature of a cosmological boson gas is less than the critical temperature, a Bose-Einstein Condensation process can always take place during the cosmic history of the universe. Zero temperature condensed dark matter can be described as a non-relativistic, Newtonian gravitational condensate, whose density and pressure are related by a barotropic equation of state, with barotropic index equal to one. In the present paper we analyze the effects of the finite dark matter temperature on the properties of the dark matter halos. We formulate the basic equations describing the finite temperature condensate, representing a generalized Gross-Pitaevskii equation that takes into account the presence of the thermal cloud. The static condensate and thermal cloud in thermodynamic equilibrium is analyzed in detail, by using the Hartree-Fock-Bogoliubov and Thomas-Fermi approximations. The condensed dark matter and thermal cloud density and mass profiles at finite temperatures are explicitly obtained. Our results show that when the temperature of the condensate and of the thermal cloud are much smaller than the critical Bose-Einstein transition temperature, the zero temperature density and mass profiles give an excellent description of the dark matter halos. However, finite temperature effects may play an important role in the early stages of the cosmological evolution of the dark matter condensates.

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“…Therefore, the BV principle has been used to provide the best approximation to the generating functional for two and multi-time correlation functions of a set of bosonic and fermionic observables [49][50][51][52]. More recently, it was used to derive a set of equations governing the dynamics of trapped Bose gases [53,54]. The point is that this principle uses the notion of least biased state, which is the best ansatz compatible with the constraints imposed on the system.…”

Section: Introductionmentioning

confidence: 99%

Anomalous density for Bose gases at finite temperature

Boudjemâa¹,

Benarous²

2011

Phys. Rev. A

102

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We analyze the behavior of the anomalous density as function of the radial distance at different temperatures in a variational framework. We show that the temperature dependence of the anomalous density agrees with the Hartree-Fock-Bogoliubov (HFB) calculations. Comparisons between the normal and the anomalous fractions at low temperature show that the latter remains higher and consequently the neglect of the anomalous density may destabilize the condensate. These results are compatible with those of Yukalov. Surprisingly, the study of the anomalous density in terms of the interaction parameter shows that the dip in the central density is destroyed for sufficiently weak interactions. We explain this effect.

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BEC from a time-dependent variational point of view

Cited by 6 publications

References 26 publications

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

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

Finite temperature effects in Bose-Einstein condensed dark matter halos

Anomalous density for Bose gases at finite temperature

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