Mean Field Limits in Strongly Confined Systems

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URI: http://hdl.handle.net/10900/59470
http://nbn-resolving.de/urn:nbn:de:bsz:21-dspace-594706
http://dx.doi.org/10.15496/publikation-894
http://nbn-resolving.org/urn:nbn:de:bsz:21-dspace-594701
http://nbn-resolving.org/urn:nbn:de:bsz:21-dspace-594705
Dokumentart: PhDThesis
Date: 2015-02
Language: English
Faculty: 7 Mathematisch-Naturwissenschaftliche Fakultät
Department: Mathematik
Advisor: Teufel, Stefan (Prof. Dr.)
Day of Oral Examination: 2015-02-12
DDC Classifikation: 510 - Mathematics
530 - Physics
Keywords: Mathematik , Physik , Bose-Einstein-Kondensation
Other Keywords: Bose-Einstein-Kondensat
Mathematische Physik
Mean Field
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Abstract:

We consider the dynamics of N interacting Bosons in three dimensions which are strongly confined in one or two directions. We analyze the mean field scaling and the nonlinear Schrödinger scaling of the interaction potential w and choose the initial wavefunction to be close to a product wavefunction. For both scalings we prove that in the mean field limit the dynamics of the N-particle system is described by a nonlinear equation in two or one dimensions. In the case of the mean field scaling this equation is the Hartree equation and for the second scaling the nonlinear Schrödinger equation. In both cases we obtain explicit bounds for the rate of convergence of the N-particle dynamics to the one-particle dynamics.

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