Understanding the instanton method via resonant states

by Nils Wagner (TU München)

Thursday 22 Jan 2026, 16:15 → 17:45 Europe/Berlin

In the study of quantum-mechanical tunneling processes, numerous approaches have been developed to determine the decay rate of states initially confined within a metastable potential region. Virtually all analytical treatments, however, fall into one of two superficially unrelated conceptual frameworks: the resonant-state approach and the instanton method. Whereas the concept of resonant states and their associated decay widths is grounded in physical reasoning by capturing the regime of uniform probability decay, the instanton method lacks such a clear physical interpretation. In this talk, I will show that these two seemingly distinct approaches are directly connected, a link that emerges from constructing functional integrals associated to generalized eigenvalue problems with sectorial boundary conditions in the complex plane.