Remark on the Dunne-Unsal relation in exact semi-classics
High Energy Physics - Theory
2017-04-18 v3 Other Condensed Matter
Mathematical Physics
math.MP
Quantum Physics
Abstract
Recently, it is realized that non-perturbative instanton effects can be generated to all orders by perturbation theory around a degenerate minima via Dunne-Unsal relation in several quantum mechanical systems. In this work we verify the Dunne-Unsal relation for resonance energy levels of one-dimensional polynomial anharmonic oscillators. We show that the relation is applicable to cubic and quartic anharmonic oscillators which are genus one potentials. However for higher order (higher genus) anharmonic potentials the relation is not satisfied and is subject to a certain extension.
Keywords
Cite
@article{arxiv.1512.08466,
title = {Remark on the Dunne-Unsal relation in exact semi-classics},
author = {Ilmar Gahramanov and Kemal Tezgin},
journal= {arXiv preprint arXiv:1512.08466},
year = {2017}
}
Comments
20 pages, v2: minor corrections, comments and refs. added, v3: minor corrections