Duality in perturbation theory and the quantum adiabatic approximation
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 recently 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.
 Publication:

Physical Review A
 Pub Date:
 November 1998
 DOI:
 10.1103/PhysRevA.58.3439
 arXiv:
 arXiv:hepth/9801069
 Bibcode:
 1998PhRvA..58.3439F
 Keywords:

 03.65.Bz;
 02.90.+p;
 Other topics in mathematical methods in physics;
 High Energy Physics  Theory;
 Condensed Matter;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology;
 Mathematical Physics;
 Nonlinear Sciences  Chaotic Dynamics;
 Quantum Physics
 EPrint:
 9 pages, revtex. Improved english and presentation. Final version accepted for publication by Physical Review A