Non-adiabatic transitions in multi-level systems

Details Non-adiabatic transitions in multi-level systems Non-adiabatic transitions in multi-level systems

1999-08-04

arxiv.org/abs/quant-ph/9908018v1

Physics

Quantum Physics

25 pages RevTeX, 9 figures and 4 tables as Postscipt files

Scientific paper

10.1103/PhysRevA.61.062104

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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