WKB Analysis of Bohmian Dynamics

Handle URI:
http://hdl.handle.net/10754/563044
Title:
WKB Analysis of Bohmian Dynamics
Authors:
Figalli, Alessio; Klein, Christian C.; Markowich, Peter A. ( 0000-0002-3704-1821 ) ; Sparber, Christof
Abstract:
We consider a semiclassically scaled Schrödinger equation with WKB initial data. We prove that in the classical limit the corresponding Bohmian trajectories converge (locally in measure) to the classical trajectories before the appearance of the first caustic. In a second step we show that after caustic onset this convergence in general no longer holds. In addition, we provide numerical simulations of the Bohmian trajectories in the semiclassical regime that illustrate the above results. © 2014 Wiley Periodicals, Inc.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
Wiley-Blackwell
Journal:
Communications on Pure and Applied Mathematics
Issue Date:
18-Oct-2013
DOI:
10.1002/cpa.21487
Type:
Article
ISSN:
00103640
Sponsors:
AF was supported by National Science Foundation Grant DMS-0969962. CK gives thanks for financial support to the ANR via the program ANR-09-BLAN-0117-01 and the project FroM-PDE funded by the European Research Council through the Advanced Investigator Grant Scheme. CS acknowledges support by the National Science Foundation through Grant DMS-1161580.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorFigalli, Alessioen
dc.contributor.authorKlein, Christian C.en
dc.contributor.authorMarkowich, Peter A.en
dc.contributor.authorSparber, Christofen
dc.date.accessioned2015-08-03T11:34:28Zen
dc.date.available2015-08-03T11:34:28Zen
dc.date.issued2013-10-18en
dc.identifier.issn00103640en
dc.identifier.doi10.1002/cpa.21487en
dc.identifier.urihttp://hdl.handle.net/10754/563044en
dc.description.abstractWe consider a semiclassically scaled Schrödinger equation with WKB initial data. We prove that in the classical limit the corresponding Bohmian trajectories converge (locally in measure) to the classical trajectories before the appearance of the first caustic. In a second step we show that after caustic onset this convergence in general no longer holds. In addition, we provide numerical simulations of the Bohmian trajectories in the semiclassical regime that illustrate the above results. © 2014 Wiley Periodicals, Inc.en
dc.description.sponsorshipAF was supported by National Science Foundation Grant DMS-0969962. CK gives thanks for financial support to the ANR via the program ANR-09-BLAN-0117-01 and the project FroM-PDE funded by the European Research Council through the Advanced Investigator Grant Scheme. CS acknowledges support by the National Science Foundation through Grant DMS-1161580.en
dc.publisherWiley-Blackwellen
dc.titleWKB Analysis of Bohmian Dynamicsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalCommunications on Pure and Applied Mathematicsen
dc.contributor.institutionDepartment of Mathematics, University of Texas at Austin, 1 University Station, C1200, Austin, TX 78712, United Statesen
dc.contributor.institutionInstitut de Mathématiques de Bourgogne, 9 avenue Alain Savary, Dijon CEDEX, 21078, Franceen
dc.contributor.institutionDepartment of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S. Morgan St., Chicago, IL, 60607, United Statesen
kaust.authorMarkowich, Peter A.en
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