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