Energy-time uncertainty principle and lower bounds on sojourn time

Joachim Asch, Olivier Bourget, Victor Cortes, Claudio Fernandez

Published 2015-07-23Version 1

One manifestation of quantum resonances is a large sojourn time, or autocorrelation, of states which are initially localized. We elaborate on Lavine's time-energy uncertainty principle and give an estimate on the sojourn time. The bound involves Fermi's Golden Rule for the case of perturbed embedded eigenstates. Only very mild regularity is required. We illustrate the theory by applications to resonances for time dependent- and multistate systems .