caa a22 4500 445320400 CHVBK 20180317142702.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00023-011-0116-1 doi (NATIONALLICENCE)springer-10.1007/s00023-011-0116-1 Stochastic Description of a Bose-Einstein Condensate [Elektronische Daten] [Laura Morato, Stefania Ugolini] 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. The Author(s), 2011 Morato Laura Facoltà di Scienze, Università di Verona, Strada le Grazie, 37134, Verona, Italy aut Ugolini Stefania Dipartimento di Matematica, Università di Milano, via Saldini, Milan, Italy aut Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/8(2011-12-01), 1601-1612 1424-0637 12:8<1601 2011 12 23 https://doi.org/10.1007/s00023-011-0116-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00023-011-0116-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Morato Laura Facoltà di Scienze, Università di Verona, Strada le Grazie, 37134, Verona, Italy aut NATIONALLICENCE 700 1- Ugolini Stefania Dipartimento di Matematica, Università di Milano, via Saldini, Milan, Italy aut NATIONALLICENCE 773 0- Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/8(2011-12-01), 1601-1612 1424-0637 12:8<1601 2011 12 23 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer