Multilevel Landau–Zener formulae: adiabatic reduction on a complex path

Gabriel Firica

Equipe de Physique Mathématique et Géométrie-UMR 9994, Université Paris 7 2 Place Jussieu, 75 251, Paris Cedex 05, France

Abstract: We consider, in the semi-classical (adiabatic) limit, evolution equations whose generators extend into a strip around real axis as a holomorphic family of operators (with respect to the time-variable). The asymptotic expansion of the $\mathbb S$-matrix associated to this evolution can be expressed in terms of simple quantities attached to the singularities for the spectrum of Hamiltonians from complex-time plane. We extend to many-level case the result from [26] which contains as limit cases both the Landau–Zener formula and Friedrichs–Hagedorn results for this problem.

Received: 17.04.1995

Language: English

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