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.
Original language | English |
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Number of pages | 38 |
Journal | Physical Review A |
Volume | 61 |
Issue number | 6 |
DOIs | |
Publication status | Published - 16 May 2000 |
Keywords
- quantum system
- adiabatic states
- branch point
- Stokes lines
- nonadiabatic transitions
- quantum
- physics