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Initial-switching refers to the way in which the decay of an initiallyconfined state begins, as the barrier isolating it from the exterior isrelaxed. We study these effects in the context of Longhi's version of theFano-Anderson model. Most authors assume the sudden approximation where thecoupling is turned on instantaneously. We consider a finite rise time T, bothnumerically and analytically. When the coupling is ramped up linearly over aswitching time T, we show that the asymptotic survival amplitude acquires aphase T and is modulated by a factor (sin T)/T. Several other results relatingto the solution of the model are obtained. All site amplitudes have the samedecay constant during the exponential decay regime. In the asymptotic regime,the amplitude and phase of decay oscillations depend on the initial-switchingprofile, but the period does not.

Memory effects induced by initial switching conditions