The Gross-Pitaevskii Hierarchy on General Rectangular Tori

Herr S, Sohinger V (2016)
Archive for Rational Mechanics and Analysis 220(3): 1119-1158.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Herr, SebastianUniBi ; Sohinger, Vedran
Abstract / Bemerkung
In this work, we study the Gross-Pitaevskii hierarchy on general-rational and irrational-rectangular tori of dimensions two and three. This is a system of infinitely many linear partial differential equations which arises in the rigorous derivation of the nonlinear Schrodinger equation. We prove a conditional uniqueness result for the hierarchy. In two dimensions, this result allows us to obtain a rigorous derivation of the defocusing cubic nonlinear Schrodinger equation from the dynamics of many-body quantum systems. On irrational tori, this question was posed as an open problem in the previous work of Kirkpatrick, Schlein, and Staffilani.
Erscheinungsjahr
2016
Zeitschriftentitel
Archive for Rational Mechanics and Analysis
Band
220
Ausgabe
3
Seite(n)
1119-1158
ISSN
0003-9527
eISSN
1432-0673
Page URI
https://pub.uni-bielefeld.de/record/2917132

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Herr S, Sohinger V. The Gross-Pitaevskii Hierarchy on General Rectangular Tori. Archive for Rational Mechanics and Analysis. 2016;220(3):1119-1158.
Herr, S., & Sohinger, V. (2016). The Gross-Pitaevskii Hierarchy on General Rectangular Tori. Archive for Rational Mechanics and Analysis, 220(3), 1119-1158. doi:10.1007/s00205-015-0950-2
Herr, S., and Sohinger, V. (2016). The Gross-Pitaevskii Hierarchy on General Rectangular Tori. Archive for Rational Mechanics and Analysis 220, 1119-1158.
Herr, S., & Sohinger, V., 2016. The Gross-Pitaevskii Hierarchy on General Rectangular Tori. Archive for Rational Mechanics and Analysis, 220(3), p 1119-1158.
S. Herr and V. Sohinger, “The Gross-Pitaevskii Hierarchy on General Rectangular Tori”, Archive for Rational Mechanics and Analysis, vol. 220, 2016, pp. 1119-1158.
Herr, S., Sohinger, V.: The Gross-Pitaevskii Hierarchy on General Rectangular Tori. Archive for Rational Mechanics and Analysis. 220, 1119-1158 (2016).
Herr, Sebastian, and Sohinger, Vedran. “The Gross-Pitaevskii Hierarchy on General Rectangular Tori”. Archive for Rational Mechanics and Analysis 220.3 (2016): 1119-1158.

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arXiv: 1410.5338

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