Nonadiabatic transitions in multilevel systems

Michael Wilkinson, Michael A. Morgan

Research output: Contribution to journalArticle

11 Citations (Scopus)

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.
LanguageEnglish
Number of pages38
JournalPhysical Review A
Volume61
Issue number6
DOIs
Publication statusPublished - 16 May 2000

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transition probabilities
energy levels
exponents
operators

Keywords

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

Cite this

Wilkinson, Michael ; Morgan, Michael A. / Nonadiabatic transitions in multilevel systems. In: Physical Review A. 2000 ; Vol. 61, No. 6.
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Nonadiabatic transitions in multilevel systems. / Wilkinson, Michael; Morgan, Michael A.

In: Physical Review A, Vol. 61, No. 6, 16.05.2000.

Research output: Contribution to journalArticle

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AB - 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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