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Averaging of nonlinear Schrödinger equations with strong magnetic confinement

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. 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.4310/CMS.2017.v15.n7.a7DOIArticle
http://www.intlpress.com/site/pub/pages/journals/items/cms/content/vols/0015/0007/a007/PublisherArticle
https://arxiv.org/abs/1611.01574arXivDiscussion Paper
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.
Funders:
Funding AgencyGrant Number
NSFDMS-1363432
Agence Nationale de la Recherche (ANR)ANR-14-CE23-0007-01
NSFDMS-1348092
Subject Keywords:nonlinear Schrödinger equation, magnetic confinement, Landau levels, averaging
Issue or Number:7
Classification Code:2000 Mathematics Subject Classification. 35Q55, 35B25
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:03 Oct 2019 17:53

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