Transition probability for multiple avoided crossings with a small gap through an exact WKB method and a microlocal approach

DOI10.1016/J.CRMA.2012.10.005zbMath1257.81029OpenAlexW2079395793MaRDI QIDQ1759784

Maher Zerzeri, Takuya Watanabe

Publication date: 22 November 2012

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2012.10.005

Mathematics Subject Classification ID

Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics (70H11)

Related Items (1)

Landau-Zener formula in a ``non-adiabatic regime for avoided crossings

Cites Work

• Proof of the Landau-Zener formula in an adiabatic limit with small eigenvalue gaps
• Precise estimates for tunneling and eigenvalues near a potential barrier
• Semiclassical representation of the scattering matrix by a Feynman integral
• Adiabatic transition probability for a tangential crossing
• Precise exponential estimates in adiabatic theory
• Semi-classical analysis for Harper's equation. III : Cantor structure of the spectrum
• Semiclassical resonances for a two-level Schrödinger operator with a conical intersection
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