Derivation of the Time Dependent Gross Pitaevskii Equation with External Fields

Peter Pickl

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arXiv · 1001.4894

Derivation of the Time Dependent Gross Pitaevskii Equation with External Fields

Peter Pickl

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Abstract

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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Peter Pickl. 2010-02-24. Derivation of the Time Dependent Gross Pitaevskii Equation with External Fields. https://arxiv.org/abs/1001.4894

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