Remark on the Dunne-Unsal relation in exact semi-classics

Understand

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.