### Abstract

Language | English |
---|---|

Number of pages | 38 |

Journal | Physical Review A |

Volume | 61 |

Issue number | 6 |

DOIs | |

Publication status | Published - 16 May 2000 |

### Fingerprint

### Keywords

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

### Cite this

*Physical Review A*,

*61*(6). https://doi.org/10.1103/PhysRevA.61.062104

}

*Physical Review A*, vol. 61, no. 6. https://doi.org/10.1103/PhysRevA.61.062104

**Nonadiabatic transitions in multilevel systems.** / Wilkinson, Michael; Morgan, Michael A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Nonadiabatic transitions in multilevel systems

AU - Wilkinson, Michael

AU - Morgan, Michael A.

PY - 2000/5/16

Y1 - 2000/5/16

N2 - 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.

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.

KW - quantum system

KW - adiabatic states

KW - branch point

KW - Stokes lines

KW - nonadiabatic transitions

KW - quantum

KW - physics

U2 - 10.1103/PhysRevA.61.062104

DO - 10.1103/PhysRevA.61.062104

M3 - Article

VL - 61

JO - Physical Review A - Atomic, Molecular, and Optical Physics

T2 - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 6

ER -