Semiclassical resonances for a two-level Schrödinger operator with a conical intersection

Setsuro Fujiié, Caroline Lasser, Laurence Nédélec

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10 Scopus citations

Abstract

We study the resonant set of a two-level Schrödinger operator with a linear conical intersection. This model operator can be decomposed into a direct sum of first order systems on the real half-line. For these ordinary differential systems we locally construct exact WKB solutions, which are connected to global solutions, amongst which are resonant states. The main results are a generalized Bohr-Sommerfeld quantization condition and an asymptotic description of the set of resonances as a distorted lattice.

Original languageEnglish
Pages (from-to)17-58
Number of pages42
JournalAsymptotic Analysis
Volume65
Issue number1-2
DOIs
StatePublished - 2009
Externally publishedYes

Keywords

  • Conical intersection
  • Exact WKB solutions
  • Resonances
  • Schrödinger systems
  • Semiclassical analysis

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