dorsal/arxiv
View SchemaNon-adiabatic transitions in multi-level systems
| Authors | Michael Wilkinson, Michael A. Morgan |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9908018 |
| URL | https://arxiv.org/abs/quant-ph/9908018 |
| DOI | 10.1103/PhysRevA.61.062104 |
Abstract
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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"abstract": "In a quantum system with a smoothly and slowly varying Hamiltonian, which\napproaches a constant operator at times $t\\to \\pm \\infty$, the transition\nprobabilities between adiabatic states are exponentially small. They are\ncharacterized by an exponent that depends on a phase integral along a path\naround a set of branch points connecting the energy level surfaces in complex\ntime. Only certain sequences of branch points contribute. We propose that these\nsequences are determined by a topological rule involving the Stokes lines\nattached to the branch points. Our hypothesis is supported by theoretical\narguments and results of numerical experiments.",
"arxiv_id": "quant-ph/9908018",
"authors": [
"Michael Wilkinson",
"Michael A. Morgan"
],
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"quant-ph"
],
"doi": "10.1103/PhysRevA.61.062104",
"title": "Non-adiabatic transitions in multi-level systems",
"url": "https://arxiv.org/abs/quant-ph/9908018"
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