Derivation of the time dependent Gross–Pitaevskii equation with external fields

Using a new method [19], it is possible to derive mean field equations from the microscopic N body Schrödinger evolution of interacting particles without using BBGKY hierarchies. This method also allows for error estimates and can be generalized to systems with external fields, of which both points...

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Bibliographic Details
Published inReviews in mathematical physics Vol. 27; no. 1; p. 1550003
Main Author Pickl, Peter
Format Journal Article
LanguageEnglish
Published Singapore World Scientific Publishing Company 01.02.2015
World Scientific Publishing Co. Pte., Ltd
Subjects
Hierarchies
Scaling
Time dependence
NLS
Gross–Pitaevskii
mean field
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ISSN0129-055X
1793-6659
DOI10.1142/S0129055X15500038

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Summary:Using a new method [19], it is possible to derive mean field equations from the microscopic N body Schrödinger evolution of interacting particles without using BBGKY hierarchies. This method also allows for error estimates and can be generalized to systems with external fields, of which both points are relevant from a physics perspective. Recently, this method was used to derive the Hartree equation for singular interactions [11] and the Gross–Pitaevskii equation without positivity condition on the interaction [17] where one had to restrict the scaling behavior of the interaction. Assuming positivity of the interaction, this paper deals with more general scalings including the so-called Gross–Pitaevskii scaling.
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ISSN:0129-055X
1793-6659
DOI:10.1142/S0129055X15500038