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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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.
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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

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