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We consider an analytical approach that involves the complex poles of thepropagator to investigate the effect due to the lack of time reversalinvariance on the time evolution of decay for purely absorptive potentials. Wefind that the choice of the initial state may change the exponential decayingregime into a nonexponential oscillatory behavior at time scales of the orderof a lifetime of the system. We illustrate this effect for a spectralsingularity corresponding to a purely imaginary delta-shell potential.

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