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Analysis and Stochastics of Growth Processes and Interface Models$
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Peter Mörters, Roger Moser, Mathew Penrose, Hartmut Schwetlick, and Johannes Zimmer

Print publication date: 2008

Print ISBN-13: 9780199239252

Published to Oxford Scholarship Online: September 2008

DOI: 10.1093/acprof:oso/9780199239252.001.0001

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Interacting Brownian Motions and the Gross-Pitaevskii Formula

Interacting Brownian Motions and the Gross-Pitaevskii Formula

(p.173) 8 Interacting Brownian Motions and the Gross-Pitaevskii Formula
Analysis and Stochastics of Growth Processes and Interface Models

Stefan Adams

Wolfgang König

Oxford University Press

Bose–Einstein condensation predicts that, under certain conditions (in particular extremely low temperature), all particles will condense into one state. Some of the physical background is surveyed in this chapter. The Gross–Pitaevskii approximation for dilute systems is also discussed. Variational problems appear here naturally, as the quantum mechanical ground state is of interest. In connection with positive temperature, related probabilistic models, based on interacting Brownian motions in a trapping potential, are introduced. Again, large deviation techniques are used to determine the mean occupation measure, both for vanishing temperature and large particle number.

Keywords:   Bose–Einstein condensation, Gross–Pitaevskii approximation, in-teracting Brownian motion, large deviation techniques

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