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

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

2005-11-30

arxiv.org/abs/math/0511724v2

Mathematics

Analysis of PDEs

45 pages 4 figures

Scientific paper

We study the resonant set of a two-level Schr\"odinger 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.

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