WKB Analysis of Bohmian Dynamics

Alessio Figalli; Christian C. Klein; Peter A. Markowich; Christof Sparber

doi:10.1002/cpa.21487

WKB Analysis of Bohmian Dynamics

Alessio Figalli, Christian C. Klein, Peter A. Markowich, Christof Sparber

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8 Scopus citations

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.

Original language	English (US)
Pages (from-to)	581-620
Number of pages	40
Journal	Communications on Pure and Applied Mathematics
Volume	67
Issue number	4
DOIs	https://doi.org/10.1002/cpa.21487
State	Published - Oct 18 2013

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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.

ASJC Scopus subject areas

Applied Mathematics
General Mathematics

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10.1002/cpa.21487

https://repository.kaust.edu.sa/bitstream/10754/563044/1/Articlefile1.pdf

Cite this

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title = "WKB Analysis of Bohmian Dynamics",

abstract = "We consider a semiclassically scaled Schr{\"o}dinger 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. {\textcopyright} 2014 Wiley Periodicals, Inc.",

author = "Alessio Figalli and Klein, {Christian C.} and Markowich, {Peter A.} and Christof Sparber",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: 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.",

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doi = "10.1002/cpa.21487",

language = "English (US)",

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AU - Figalli, Alessio

AU - Klein, Christian C.

AU - Markowich, Peter A.

AU - Sparber, Christof

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: 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.

PY - 2013/10/18

Y1 - 2013/10/18

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/563044

UR - http://arxiv.org/pdf/1202.3134

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U2 - 10.1002/cpa.21487

DO - 10.1002/cpa.21487

M3 - Article

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EP - 620

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

IS - 4

ER -

WKB Analysis of Bohmian Dynamics

Abstract

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