Time evolution of decay for purely absorptive potentials: The effect of spectral singularities

TL;DR

This paper investigates how spectral singularities influence the decay dynamics of purely absorptive potentials, revealing that initial states can induce nonexponential oscillations instead of standard exponential decay.

Contribution

It introduces an analytical method using complex poles to study decay evolution, highlighting the impact of spectral singularities on decay behavior.

Findings

Initial states can alter decay from exponential to oscillatory.

Spectral singularities cause nonexponential decay patterns.

The approach applies to purely imaginary delta-shell potentials.

Abstract

We consider an analytical approach that involves the complex poles of the propagator to investigate the effect due to the lack of time reversal invariance on the time evolution of decay for purely absorptive potentials. We find that the choice of the initial state may change the exponential decaying regime into a nonexponential oscillatory behavior at time scales of the order of a lifetime of the system. We illustrate this effect for a spectral singularity corresponding to a purely imaginary delta-shell potential.