Initial state maximizing the nonexponentially decaying survival probability for unstable multilevel systems

Abstract

The long-time behavior of the survival probability for unstable multilevel systems that follows the power-decay law is studied based on the $N$-level Friedrichs model, and is shown to depend on the initial population in unstable states. A special initial state maximizing the asymptote of the survival probability at long times is found and examined by considering the spontaneous-emission process for the hydrogen atom interacting with the electromagnetic field.