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On the derivation of the Gross-Pitaevskii equation

Riccardo Adami — 2005

Bollettino dell'Unione Matematica Italiana

This article reflects in its content the talk the author gave at the XVII Congresso dell’Unione Matematica Italiana, held in Milano, 8-13 September 2003. We review about some recent results on the problem of deriving the Gross-Pitaevskii equation in dimension one from the dynamics of a quantum system with a large number of identical bosons. We explain the motivations for some peculiar choices (shape of the interaction potential, scaling, initial datum). Open problems are pointed out and difficulties...

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