Preprint 77/2007

Interacting Brownian motions and the Gross-Pitaevskii formula

Stefan Adams and Wolfgang König

Contact the author: Please use for correspondence this email.
Submission date: 01. Sep. 2007
Pages: 22
published 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 / P. Mörters (ed.)
Oxford : Oxford University Press, 2008. - P. 173 - 193 
MSC-Numbers: 60F10, 60J65, 82B10, 82B26
Keywords and phrases: large deviations, Gross-Pitaevskii-formula, interacting brownian motions, Bosons
Download full preprint: PDF (249 kB), PS ziped (244 kB)

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.

23.06.2018, 02:11