Objetivo We plan to derive rigorously the one-particle Gross-Pitaevskii equation (GPE) as a peculiar limit of a N-particles Schrödinger equation and to study models where the quantum decoherence is induced by the scattering. More specifically, we shall consider a s ystem of N particles interacting one another by means of a suitable potential and perform the limit for the range of the potential shrinking to zero as N goes to infinity. We are confident that in that limit the dynamics of the particles factorises and tha t for the single particle the effective evolution is given by the GPE. Thereafter we shall employ the result obtained and the techniques developed in order to construct quantum models in which the decoherence induced by scattering is apparent and can be co mputed with an explicit estimate of the error. The work plan can be summarized as follows: 1. Derivation of the GPE in dimension one from a system of particles interacting one another through a Dirac delta potential. 2. Derivation of the GPE in dimension t wo, again with delta potentials. Here the challenge is to deal with an "exotic" energy space in which no classical estimate holds. 3. Analysis of the problem in dimension three. In this case the strategy with delta potentials cannot work since the Hamilton ian for the interacting N-particles system is not well-defined. So our investigation shall be performed either directly by means of a more realistic potential, or by introducing a confining potential which "mitigates" the effects of the Dirac deltas. 4. Co nstruction of models of the type "system+environment", where the system consists of one (or a finite number of) heavy particle(s) and the environment is modeled by N light particles. Then we shall study the decoherence effect induced by the environment on the system through the mechanism of the multiple scattering. 5. Application of such models to problems of semiclassical limit. Ámbito científico natural sciencesphysical sciencesquantum physicsnatural sciencesphysical sciencescondensed matter physicsbose-einstein condensates Programa(s) FP6-MOBILITY - Human resources and Mobility in the specific programme for research, technological development and demonstration "Structuring the European Research Area" under the Sixth Framework Programme 2002-2006 Tema(s) MOBILITY-4.1 - Marie Curie European Reintegration Grants (ERG) Convocatoria de propuestas FP6-2002-MOBILITY-11 Consulte otros proyectos de esta convocatoria Régimen de financiación ERG - Marie Curie actions-European Re-integration Grants Coordinador UNIVERSITÀ DEGLI STUDI DI ROMA 'LA SAPIENZA' Aportación de la UE Sin datos Dirección Piazzale Aldo Moro 2 ROMA Italia Ver en el mapa Coste total Sin datos
