This article reflects in its content the talk the author gave at the XVII Congresso dellUnione 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.
Il presente articolo riproduce nel contenuto la conferenza che l'autore ha tenuto al XVII Congresso dellUnione Matematica Italiana, svoltosi a Milano, 8-13 settembre 2003. Vengono presentati alcuni recenti risultati sul problema della derivazione dellequazione di Gross-Pitaevskii in dimensione uno a partire dalla dinamica di un sistema quantistico che contiene un grande numero di bosoni identici. Sono spiegati i motivi per alcune scelte particolari (forma del potenziale di interazione, riscalamento, dato iniziale). Sono evidenziati i problemi aperti e sottolineate le difficoltà e gli ostacoli allapplicazione della stessa strategia in dimensione superiore.
@article{BUMI_2005_8_8B_2_359_0,
author = {Riccardo Adami},
title = {On the derivation of the Gross-Pitaevskii equation},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {8-A},
year = {2005},
pages = {359-368},
zbl = {1178.35309},
mrnumber = {2149389},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2005_8_8B_2_359_0}
}
Adami, Riccardo. On the derivation of the Gross-Pitaevskii equation. Bollettino dell'Unione Matematica Italiana, Tome 8-A (2005) pp. 359-368. http://gdmltest.u-ga.fr/item/BUMI_2005_8_8B_2_359_0/
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