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Interacting Brownian motions and the Gross-Pitaevskii formula
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Adams, S. (Stefan) and König, Wolfgang (2008) Interacting Brownian motions and the Gross-Pitaevskii formula. In: Mörters, Peter and Moser, Roger and Penrose, Mathew and Schwetlick, Hartmut and Zimmer, Johannes, (eds.) Analysis and stochastics of growth processes and interface models. Oxford: Oxford University Press, pp. 173-193. ISBN 9780199239252
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Official URL: http://dx.doi.org/10.1093/acprof:oso/9780199239252...
Abstract
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.
Item Type: | Book Item | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Publisher: | Oxford University Press | ||||
Place of Publication: | Oxford | ||||
ISBN: | 9780199239252 | ||||
Book Title: | Analysis and stochastics of growth processes and interface models | ||||
Editor: | Mörters, Peter and Moser, Roger and Penrose, Mathew and Schwetlick, Hartmut and Zimmer, Johannes | ||||
Official Date: | 2008 | ||||
Dates: |
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Number of Pages: | 336 | ||||
Page Range: | pp. 173-193 | ||||
DOI: | 10.1093/acprof:oso/9780199239252.003.0008 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
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