Semiclassical resonances for a two-level Schr'odinger operator with a conical intersection

摘要

We study the resonant set of a two-level Schr\"odinger operator with a linearconical intersection. This model operator can be decomposed into a direct sumof first order systems on the real half-line. For these ordinary differentialsystems we locally construct exact WKB solutions, which are connected to globalsolutions, amongst which are resonant states. The main results are ageneralized Bohr-Sommerfeld quantization condition and an asymptoticdescription of the set of resonances as a distorted lattice.