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Accueil du site > Publications > Publications 2006 > Dynamics of the Bose-Einstein condensation : analogy with the collapse dynamics of a classical self-gravitating Brownian gas

Dynamics of the Bose-Einstein condensation : analogy with the collapse dynamics of a classical self-gravitating Brownian gas

Julien Sopik, Clément Sire, and Pierre-Henri Chavanis

par Clément Sire - 11 avril 2006

We consider the dynamics of a gas of free bosons within a semi-classical Fokker-Planck equation for which we give a physical justification. In this context, we find a striking similarity between the Bose-Einstein condensation in the canonical ensemble, and the gravitational collapse of a gas of classical self-gravitating Brownian particles. The paper is mainly devoted to the complete study of the Bose-Einstein “collapse” within this model. We find that at the Bose-Einstein condensation temperature T_c, the chemical potential \mu(t) vanishes exponentially with a universal rate that we compute exactly. Below T_c, we show analytically that \sqrt{\mu(t)} vanishes linearly in a finite time t_{coll}. After t_{coll}, the mass of the condensate grows linearly with time and saturates exponentially to its equilibrium value for large time. We also give analytical results for the density scaling functions, for the corrections to scaling, and for the exponential relaxation time. Finally, we find that the equilibration time (above T_c) and the collapse time t_{boll} (below T_c), both behave like -T_c^{-3}\ln|T-T_c|, near T_c.

http://xxx.lanl.gov/abs/cond-mat/0511347