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Interacting Brownian motions and the Gross-Pitaevskii formula
Stefan Adams and Wolfgang KönigAbstract
We review probabilistic approaches to the Gross-Pitaevskii theory describing interacting dilute systems of particles. The main achievement are large deviations principles for the mean occupation measure of a large system of interacting Brownian motions in a trapping potential. The corresponding rate functions are given as variational problems whose solution provide effective descriptions of the infinite system.
- Received:
- 01.09.07
- Published:
- 01.09.07
- MSC Codes:
- 60F10, 60J65, 82B10, 82B26
- Keywords:
- large deviations, Gross-Pitaevskii-formula, interacting brownian motions, Bosons
Related publications
Interacting Brownian motions and the Gross-Pitaevskii formula
In: Analysis and stochastics of growth processes and interface models : selected papers based on the presentations at a regional meeting of the London Mathematical Society and a workshop on `Analysis and stochastics of growth processes', Bath, UK, September 11-15, 2006 / Peter Mörters (ed.)Oxford : Oxford University Press, 2008. - pp. 173-193