Semiclassical asymptotics for weakly nonlinear Bloch waves

Rémi Carles, Peter A. Markowich, Christof Sparber

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


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 languageEnglish (US)
Pages (from-to)343-375
Number of pages33
JournalJournal of Statistical Physics
Issue number1-2
StatePublished - Oct 2004
Externally publishedYes

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: 2Institut für Mathematik der Universität Wien Nordbergstraße 15, A-1090 Vienna, Austria; e-mail:; e-mail: 3On leave from MAB, Université Bordeaux 1.


  • 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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