Abstract
We present microscopic derivations of the defocusing two-dimensional cubic nonlinear Schrodinger equation and the Gross-Pitaevskii equation starting from an interacting N-particle system of bosons. We consider the interaction potential to be given either by W beta(x) = N -1+2 beta W(N beta x), for any beta > 0, or to be given by V-N (x) = e(2N) V(e(N) x), for some spherical symmetric, nonnegative and compactly supported W, V. L-infinity (R-2, R). In both cases we prove the convergence of the reduced density corresponding to the exact time evolution to the projector onto the solution of the corresponding nonlinear Schrodinger equation in trace norm. For the latter potential V-N we show that it is crucial to take the microscopic structure of the condensate into account in order to obtain the correct dynamics.
Item Type: | Journal article |
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Faculties: | Mathematics, Computer Science and Statistics > Mathematics |
Subjects: | 500 Science > 510 Mathematics |
ISSN: | 0010-3616 |
Language: | English |
Item ID: | 82351 |
Date Deposited: | 15. Dec 2021, 15:01 |
Last Modified: | 13. Aug 2024, 12:43 |