Frank, Rupert L. and Méhats, Florian and Sparber, Christof (2017) Averaging of nonlinear Schrödinger equations with strong magnetic confinement. Communications in Mathematical Sciences, 15 (7). pp. 1933-1945. ISSN 1539-6746. doi:10.4310/CMS.2017.v15.n7.a7. https://resolver.caltech.edu/CaltechAUTHORS:20170428-154120889
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Abstract
We consider the dynamics of nonlinear Schrödinger equations with strong constant magnetic fields. In an asymptotic scaling limit the system exhibits a purely magnetic confinement, based on the spectral properties of the Landau Hamiltonian. Using an averaging technique we derive an associated effective description via an averaged model of nonlinear Schrödinger type. In a special case this also yields a derivation of the LLL equation.
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| Additional Information: | © 2017 International Press. Paper received on 15 March 2017; Paper accepted on 30 June 2017. R.L.F. has been supported by the U.S. National Science Foundation through grant no. DMS-1363432. F.M. acknowledges support by the ANR project Moonrise ANR-14-CE23-0007-01. C.S. has been supported by the U.S. National Science Foundation through grant no. DMS-1348092. | ||||||||||||
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| Subject Keywords: | nonlinear Schrödinger equation, magnetic confinement, Landau levels, averaging | ||||||||||||
| Issue or Number: | 7 | ||||||||||||
| Classification Code: | 2000 Mathematics Subject Classification. 35Q55, 35B25 | ||||||||||||
| DOI: | 10.4310/CMS.2017.v15.n7.a7 | ||||||||||||
| Record Number: | CaltechAUTHORS:20170428-154120889 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170428-154120889 | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 77070 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | Tony Diaz | ||||||||||||
| Deposited On: | 28 Apr 2017 23:50 | ||||||||||||
| Last Modified: | 15 Nov 2021 17:27 |
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