Publication Date:
2011-06-06
Description:
In this work we give a positive answer to the following question: does Stochastic Mechanics uniquely define a three-dimensional stochastic process which describes the motion of a particle in a Bose–Einstein condensate? To this extent we study a system of N trapped bosons with pair interaction at zero temperature under the Gross–Pitaevskii scaling, which allows to give a theoretical proof of Bose–Einstein condensation for interacting trapped gases in the limit of N going to infinity. We show that under the assumption of strictly positivity and continuous differentiability of the many-body ground state wave function it is possible to rigorously define a one-particle stochastic process, unique in law, which describes the motion of a single particle in the gas and we show that, in the scaling limit, the one-particle process continuously remains outside a time dependent random “interaction-set” with probability one. Moreover, we prove that its stopped version converges, in a relative entropy sense, toward a Markov diffusion whose drift is uniquely determined by the order parameter, that is the wave function of the condensate. Content Type Journal Article Pages 1-12 DOI 10.1007/s00023-011-0116-1 Authors Laura M. Morato, Facoltà di Scienze, Università di Verona, Strada le Grazie, 37134 Verona, Italy Stefania Ugolini, Dipartimento di Matematica, Università di Milano, via Saldini, Milan, Italy Journal Annales Henri Poincare Online ISSN 1424-0661 Print ISSN 1424-0637
Print ISSN:
1424-0637
Electronic ISSN:
1424-0661
Topics:
Mathematics
,
Physics
