On the derivation of the Gross-Pitaevskii equation

Riccardo Adami

Bollettino dell'Unione Matematica Italiana (2005)

  • Volume: 8-B, Issue: 2, page 359-368
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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Adami, Riccardo. "On the derivation of the Gross-Pitaevskii equation." Bollettino dell'Unione Matematica Italiana 8-B.2 (2005): 359-368. <http://eudml.org/doc/195880>.

@article{Adami2005,
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.},
author = {Adami, Riccardo},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {359-368},
publisher = {Unione Matematica Italiana},
title = {On the derivation of the Gross-Pitaevskii equation},
url = {http://eudml.org/doc/195880},
volume = {8-B},
year = {2005},
}

TY - JOUR
AU - Adami, Riccardo
TI - On the derivation of the Gross-Pitaevskii equation
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/6//
PB - Unione Matematica Italiana
VL - 8-B
IS - 2
SP - 359
EP - 368
AB - 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.
LA - eng
UR - http://eudml.org/doc/195880
ER -

References

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