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

Article type: Research Article

Authors: Fujiié, Setsuro^; | Lasser, Caroline^{; ;} | Nédélec, Laurence^;

Affiliations: Graduate School of Material Science, University of Hyogo, 2167 Shosha, Himeji, 671-2201 Japan. E-mail: fujiie@sci.u-hyogo.ac.jp | Fachbereich Mathematik, Freie Universität Berlin, Arnimallee 2-6, D-14195 Berlin, Germany. E-mail: lasser@math.fu-berlin.de | L.A.G.A., Institut Galilée, Université de Paris Nord, av. J.B. Clement, F-93430 Villetaneuse, France. E-mail: nedelec@math.univ-paris13.fr

Note: [] Supported by MSRI and JSPS. KAKENHI15540149.

Note: [] Supported in part by DFG priority program 1095.

Note: [] Corresponding author.

Note: [] Supported in part by the FIM of ETHZ.

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.

Keywords: conical intersection, exact WKB solutions, resonances, semiclassical analysis, Schrödinger systems

DOI: 10.3233/ASY-2009-0946

Journal: Asymptotic Analysis, vol. 65, no. 1-2, pp. 17-58, 2009