DERIVATION OF THE TWO-DIMENSIONAL NONLINEAR SCHRÖDINGER EQUATION FROM MANY BODY QUANTUM DYNAMICS.
In: American Journal of Mathematics, Jg. 133 (2011-02-01), Heft 1, S. 91-130
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Zugriff:
We derive rigorously, for both ℝ² and [-L, L]x2 the cubic nonlinear Schrödinger equation in a suitable scaling limit from the two-dimensional many-body Bose systems with short-scale repulsive pair interactions. We first prove convergence of the solution of the BBGKY hierarchy, corresponding to the many-body systems, to a solution of the infinite Gross-Pitaevskii hierarchy, corresponding to the cubic NLS; and then we prove uniqueness for the infinite hierarchy, which requires number-theoretical techniques in the periodic case. [ABSTRACT FROM AUTHOR]
Titel: |
DERIVATION OF THE TWO-DIMENSIONAL NONLINEAR SCHRÖDINGER EQUATION FROM MANY BODY QUANTUM DYNAMICS.
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Autor/in / Beteiligte Person: | Kirkpatrick, Kay ; Schlein, Benjamin ; Staffilani, Gigliola |
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Zeitschrift: | American Journal of Mathematics, Jg. 133 (2011-02-01), Heft 1, S. 91-130 |
Veröffentlichung: | 2011 |
Medientyp: | academicJournal |
ISSN: | 0002-9327 (print) |
DOI: | 10.1353/ajm.2011.0004 |
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