Derivation of the Time Dependent Gross Pitaevskii Equation with External Fields

Details Derivation of the Time Dependent Gross Pitaevskii Equation with External Fields Derivation of the Time Dependent Gross Pitaevskii Equation with External Fields

2010-01-27

arxiv.org/abs/1001.4894v2

Physics

Mathematical Physics

65 pages

Scientific paper

Using a new method [9] it is possible to derive mean field equations from the microscopic N-body Schrodinger evolution of interacting particles without using BBGKY hierarchies. Recently this method was used to derive the Hartree equation for singular interactions [4] and the Gross Pitaevskii equation without positivity condition on the interaction [10] where one had to restrict the scaling behaviour of the interaction. In this paper more general scalings shall be considered assuming positivity of the interaction.

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