Duality in Perturbation Theory and the Quantum Adiabatic Approximation
High Energy Physics - Theory
2016-09-06 v3 chao-dyn
Condensed Matter
General Relativity and Quantum Cosmology
High Energy Physics - Phenomenology
Mathematical Physics
math.MP
Chaotic Dynamics
Quantum Physics
Abstract
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.
Cite
@article{arxiv.hep-th/9801069,
title = {Duality in Perturbation Theory and the Quantum Adiabatic Approximation},
author = {Marco Frasca},
journal= {arXiv preprint arXiv:hep-th/9801069},
year = {2016}
}
Comments
9 pages, revtex. Improved english and presentation. Final version accepted for publication by Physical Review A