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 and hindrances in replicating the strategy in higher dimension are put in evidence.

Adami, R. (2005). On the derivation of the Gross-Pitaevskii equation. BOLLETTINO DELL'UNIONE MATEMATICA ITALIANA. B, 8(2), 359-368.

On the derivation of the Gross-Pitaevskii equation

ADAMI, RICCARDO
2005

Abstract

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 and hindrances in replicating the strategy in higher dimension are put in evidence.
Articolo in rivista - Articolo scientifico
Gross-Pitaevskii equation
English
359
368
Adami, R. (2005). On the derivation of the Gross-Pitaevskii equation. BOLLETTINO DELL'UNIONE MATEMATICA ITALIANA. B, 8(2), 359-368.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/11567
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