Nonadiabatic transitions in multilevel systems

Wilkinson, Michael and Morgan, Michael A. (2000) Nonadiabatic transitions in multilevel systems. Physical Review A, 61 (6). ISSN 1050-2947 (https://doi.org/10.1103/PhysRevA.61.062104)

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Abstract

In a quantum system with a smoothly and slowly varying Hamiltonian, which approaches a constant operator at times t→±∞, the transition probabilities between adiabatic states are exponentially small. They are characterized by an exponent that depends on a phase integral along a path around a set of branch points connecting the energy-level surfaces in complex time. Only certain sequences of branch points contribute. We propose that these sequences are determined by a topological rule involving the Stokes lines attached to the branch points. Our hypothesis is supported by theoretical arguments and results of numerical experiments.

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