Semiclassical asymptotics for weakly nonlinear Bloch waves

Rémi Carles; Peter A. Markowich; Christof Sparber

doi:10.1023/B:JOSS.0000044070.34410.17

Semiclassical asymptotics for weakly nonlinear Bloch waves

Rémi Carles, Peter A. Markowich, Christof Sparber

Research output: Contribution to journal › Article › peer-review

31 Scopus citations

Abstract

We study the simultaneous semi-classical and adiabatic asymptotics for a class of (weakly) nonlinear Schrödinger equations with a fast periodic potential and a slowly varying confinement potential. A rigorous two-scale WKB-analysis, locally in time, is performed. The main nonlinear phenomenon is a modification of the Berry phase.

Original language	English (US)
Pages (from-to)	343-375
Number of pages	33
Journal	Journal of Statistical Physics
Volume	117
Issue number	1-2
DOIs	https://doi.org/10.1023/B:JOSS.0000044070.34410.17
State	Published - Oct 2004
Externally published	Yes

Bibliographical note

Funding Information:
2000 Mathematics Subject Classification: 81Q20, 34E13, 34E20, 35Q55. This work was partially supported by the EU network HYKE (Contract No. HPRN-CT-2002-00282), the Wittgenstein Award 2000 of P. A. M. (funded by the Austrian research fund FWF), and the Wissenschaftskolleg Differentialgleichungen (FWF Project No. W8). 1IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes France; e-mail: [email protected] 2Institut für Mathematik der Universität Wien Nordbergstraße 15, A-1090 Vienna, Austria; e-mail: [email protected]; e-mail: [email protected] 3On leave from MAB, Université Bordeaux 1.

Keywords

Bloch eigenvalue problem
Bose-Einstein condensate
Nonlinear Schrödinger equation
WKB-asymptotics

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1023/B:JOSS.0000044070.34410.17

Cite this

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title = "Semiclassical asymptotics for weakly nonlinear Bloch waves",

abstract = "We study the simultaneous semi-classical and adiabatic asymptotics for a class of (weakly) nonlinear Schr{\"o}dinger equations with a fast periodic potential and a slowly varying confinement potential. A rigorous two-scale WKB-analysis, locally in time, is performed. The main nonlinear phenomenon is a modification of the Berry phase.",

keywords = "Bloch eigenvalue problem, Bose-Einstein condensate, Nonlinear Schr{\"o}dinger equation, WKB-asymptotics",

author = "R{\'e}mi Carles and Markowich, {Peter A.} and Christof Sparber",

note = "Funding Information: 2000 Mathematics Subject Classification: 81Q20, 34E13, 34E20, 35Q55. This work was partially supported by the EU network HYKE (Contract No. HPRN-CT-2002-00282), the Wittgenstein Award 2000 of P. A. M. (funded by the Austrian research fund FWF), and the Wissenschaftskolleg Differentialgleichungen (FWF Project No. W8). 1IRMAR, Universit{\'e} de Rennes 1, Campus de Beaulieu, 35042 Rennes France; e-mail: [email protected] 2Institut f{\"u}r Mathematik der Universit{\"a}t Wien Nordbergstra{\ss}e 15, A-1090 Vienna, Austria; e-mail: [email protected]; e-mail: [email protected] 3On leave from MAB, Universit{\'e} Bordeaux 1.",

year = "2004",

month = oct,

doi = "10.1023/B:JOSS.0000044070.34410.17",

language = "English (US)",

volume = "117",

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T1 - Semiclassical asymptotics for weakly nonlinear Bloch waves

AU - Carles, Rémi

AU - Markowich, Peter A.

AU - Sparber, Christof

N1 - Funding Information: 2000 Mathematics Subject Classification: 81Q20, 34E13, 34E20, 35Q55. This work was partially supported by the EU network HYKE (Contract No. HPRN-CT-2002-00282), the Wittgenstein Award 2000 of P. A. M. (funded by the Austrian research fund FWF), and the Wissenschaftskolleg Differentialgleichungen (FWF Project No. W8). 1IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes France; e-mail: [email protected] 2Institut für Mathematik der Universität Wien Nordbergstraße 15, A-1090 Vienna, Austria; e-mail: [email protected]; e-mail: [email protected] 3On leave from MAB, Université Bordeaux 1.

PY - 2004/10

Y1 - 2004/10

N2 - We study the simultaneous semi-classical and adiabatic asymptotics for a class of (weakly) nonlinear Schrödinger equations with a fast periodic potential and a slowly varying confinement potential. A rigorous two-scale WKB-analysis, locally in time, is performed. The main nonlinear phenomenon is a modification of the Berry phase.

AB - We study the simultaneous semi-classical and adiabatic asymptotics for a class of (weakly) nonlinear Schrödinger equations with a fast periodic potential and a slowly varying confinement potential. A rigorous two-scale WKB-analysis, locally in time, is performed. The main nonlinear phenomenon is a modification of the Berry phase.

KW - Bloch eigenvalue problem

KW - Bose-Einstein condensate

KW - Nonlinear Schrödinger equation

KW - WKB-asymptotics

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DO - 10.1023/B:JOSS.0000044070.34410.17

M3 - Article

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VL - 117

SP - 343

EP - 375

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 1-2

ER -

Semiclassical asymptotics for weakly nonlinear Bloch waves

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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