2019/09/09 by Takuya Watanabe, Watanabe, Takuya, Maher Zerzeri +1 · 1 citation
Mathematics · Physics and Astronomy · #81Q05 (34E20 34M60 81Q20) #FOS: Physical sciences #Mathematical Physics (math-ph) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · doi:10.48550/arxiv.1909.03933
openalex publication_date 2019/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a two-level transition probability for a finite number of avoided crossings with a small interaction. Landau-Zener formula, which gives the transition probability for one avoided crossing as e^-π\fracε2h, implies that the parameter h and the interaction ε play an opposite role when both tend to 0. The exact WKB method produces a generalization of that formula under the optimal regime (h)/(ε2) tends to~0. In this paper, we investigate the case (ε2)/(h) tends to 0, called "non-adiabatic" regime. This is done by reducing the associated Hamiltonian to a microlocal branching model which gives us the asymptotic expansions of the local transfer matrices.