Wednesday, October 3, 2012

1210.0253 (D. -A. Deckert et al.)

Effective Dynamics of a Heavy Particle in an Ideal Bose Gas in the
Thermodynamic Limit

D. -A. Deckert, J. Fröhlich, P. Pickl, A. Pizzo
We study a system of a heavy quantum particle, from now on called tracer particle, coupled to an ideal gas of $N$ light Bose particles with a ratio between the masses of the tracer particle and of a gas particle being proportional to the gas particle density. While all particles obey the non-relativistic dispersion relation, the tracer particle is also driven by an external potential and couples to the gas particles through a pair potential. We compare the corresponding quantum dynamics to effective dynamics, given by a Newtonian equation for the tracer particle and a corresponding effective equation for the Bose gas. We quantify the closeness of these two dynamics depending on the gas particle density and the volume of the support of their wave function. The provided estimates are such that we get convergence in any limit taking the density and the volume to infinity. In particular, they allow to interchange the thermodynamic with the mean field limit.
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