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

2005/11/30 by Setsuro Fujiié, Caroline Lasser, Fujiie, S. +3 · 1 citation
Physics and Astronomy · #33P99 #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.math/0511724

openalex publication_date 2005/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A class of analytic perturbations for one-body Schrödinger Hamiltonians

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• Bohr--Sommerfeld rules for systems

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