Anomalous time evolution due to exceptional point at the continuum threshold

Abstract

Owing to strong technological progress, many once-elusive quantum effects have been experimentally verified in recent years, including subtle deviations from the usual exponential decay law that describes quantum evolution under typical circumstances. It is theoretically understood that long-time deviations from exponential decay are attributed to the existence of a lower threshold on the continuum that describes the environmental degrees of freedom in open systems. Another circumstance under which exponential decay is modified occurs in the vicinity of a so-called exceptional point, at which two eigenvalues (and their respective eigenfunctions) coalesce. In this study, we demonstrate that in the unusual circumstance that an exceptional point appears directly at the continuum threshold, the time evolution is drastically modified and the usual exponential decay vanishes entirely.