Energy-time uncertainty principle and lower bounds on sojourn time

TL;DR

This paper explores the energy-time uncertainty principle in quantum mechanics, providing explicit bounds on sojourn time for localized states, with applications to various resonant systems including time-dependent and multistate scenarios.

Contribution

It extends Lavine's uncertainty principle by deriving explicit sojourn time bounds involving Fermi's Golden Rule for a broad class of systems.

Findings

Explicit sojourn time bounds involving Fermi's Golden Rule

Application to time-dependent systems like AC Stark effect

Analysis of resonances in multistate quantum systems

Abstract

One manifestation of quantum resonances is a large sojourn time, or autocorrelation, for states which are initially localized. We elaborate on Lavine's time-energy uncertainty principle and give an estimate on the sojourn time. For the case of perturbed embedded eigenstates the bound is explicit and involves Fermi's Golden Rule. It is valid for a very general class of systems. We illustrate the theory by applications to resonances for time dependent systems including the AC Stark effect as well as multistate systems.