Memory effects induced by initial switching conditions

TL;DR

This paper investigates how the initial switching profile, especially finite ramp times, affects the decay dynamics in the Fano-Anderson model, revealing phase shifts and modulation effects on survival amplitudes.

Contribution

It provides analytical and numerical analysis of finite ramp time effects on decay in the Fano-Anderson model, extending beyond the sudden approximation.

Findings

Survival amplitude gains a phase proportional to the ramp time T.

Amplitude modulation factor is (sin T)/T during ramp-up.

Decay constant remains the same during exponential decay regime.

Abstract

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.