# The Gross-Pitaevskii Hierarchy on General Rectangular Tori

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

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Einrichtung
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
Zeitschriftentitel
Archive for Rational Mechanics and Analysis
Band
220
Ausgabe
3
Seite(n)
1119-1158
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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