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Non-adiabatic transitions in multi-level systems

Michael Wilkinson·Michael A. Morgan
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Abstract

In a quantum system with a smoothly and slowly varying Hamiltonian, which approaches a constant operator at times $t\to \pm \infty$, 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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Michael Wilkinson, Michael A. Morgan. 1999-08-04. Non-adiabatic transitions in multi-level systems. https://doi.org/10.1103/physreva.61.062104

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