Duality in Perturbation Theory and the Quantum Adiabatic Approximation

Details Duality in Perturbation Theory and the Quantum Adiabatic Approximation Duality in Perturbation Theory and the Quantum Adiabatic Approximation

1998-01-12

arxiv.org/abs/hep-th/9801069v3

Phys.Rev. A58 (1998) 3439

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, revtex. Improved english and presentation. Final version accepted for publication by Physical Review A

Scientific paper

10.1103/PhysRevA.58.3439

Duality is considered for the perturbation theory by deriving, given a series solution in a small parameter, its dual series with the development parameter being the inverse of the other. A dual symmetry in perturbation theory is identified. It is then shown that the dual to the Dyson series in quantum mechanics is given by a recent devised series having the adiabatic approximation as leading order. A simple application of this result is given by rederiving a theorem for strongly perturbed quantum systems.

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