Local scattering matrix for a degenerate avoided-crossing in the non-coupled regime

2023/06/27 by Kenta Higuchi, Higuchi, Kenta
Mathematics · Physics and Astronomy · #35Q40 (Secondary) #81Q20 (Primary) 35B40 #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2306.15465

openalex publication_date 2023/06/27 · openalex created_date 2023/06/29 · openalex updated_date 2026/07/28

Abstract

A Landau-Zener type formula for a degenerate avoided-crossing is studied in the non-coupled regime. More precisely, a 2×2 system of first order h-differential operator with O(ε) off-diagonal part is considered in 1D. Asymptotic behavior as ε h^m/(m+1)→0⁺ of the local scattering matrix near an avoided-crossing is given, where m stands for the contact order of two curves of the characteristic set. A generalization including the cases with vanishing off-diagonals and non-Hermitian symbols is also given.

Related

• Landau-Zener Formula in a "Non-Adiabatic" regime for avoided crossings
• A microlocal Cauchy problem through a crossing point of Hamiltonian flows
• Bohr-Sommerfeld phases for avoided crossings
• Non-perturbative features of driven scattering systems
• Nonlinear Propagation of Coherent States through Avoided Energy Level Crossing