The Density Distribution of a Trapped Bose Condensed Gas at Finite Temperatures

徹郎 二国

徹郎 二国

Manas Kulkarni, Satya N. Majumdar, Grégory Schehr

We compute the full probability distribution of the moment of inertia I \propto \sum_{i=1}^N \vec{r}_i^{\,2} I ∝ ∑ i = 1 N r → i 2 of a gas of N N noninteracting bosons trapped in a harmonic potential V(r) = (1/2)\, m\, \omega^2 r^2 V ( r ) = ( 1 / 2 ) m ω 2 r 2 , in all dimensions and at all temperature. The appropriate thermodynamic limit in a trapped Bose gas consists in taking the limit N\to ∞ N → ∞ and \omega\to 0 ω → 0 with their product \rho = N \omega^d ρ = N ω d fixed, where \rho ρ plays the role analogous to the density in a translationally invariant system. In this thermodynamic limit and in dimensions d;gt 1 d > 1 , the harmonically trapped Bose gas undergoes a Bose-Einstein condensation (BEC) transition as the density \rho ρ crosses a critical value \rho_c(\beta) ρ c ( β ) , where \beta β denotes the inverse temperature. We show that the nature of the condensation is different for 1<d≤ 2 1 < d ≤ 2 and d;gt 2

Kalai Kumar Rajagopal, Patrizia Vignolo, Monica Tosi

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.

Martin Fliesser, Robert Graham