Nonadiabatic transitions in multilevel systems

Michael Wilkinson, Michael A. Morgan

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)
61 Downloads (Pure)


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.
Original languageEnglish
Number of pages38
JournalPhysical Review A
Issue number6
Publication statusPublished - 16 May 2000


  • quantum system
  • adiabatic states
  • branch point
  • Stokes lines
  • nonadiabatic transitions
  • quantum
  • physics


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