Exponential and nonexponential buildup in resonant tunneling
Roberto Romo, Alberto Hernández, and Jorge Villavicencio
Accepted
The exponential and non-exponential regimes of the buildup process in resonant tunneling structures are analyzed by considering an analytic solution of the time-dependent Schrödinger equation. It is found that the buildup exhibits a purely exponential behavior in a finite time interval followed by a clear transition to a non-exponential regime. The buildup of the probability amplitude in the non-exponential regime follows a t-3/2 time-dependence, in the same fashion as the survival amplitude in quantum decay. For incidence energies at higher isolated resonances, E=en with n > 1, it is found that the exponential regime is split into two exponential sub regimes: the first one is governed by the width Gn of the resonance chosen for the incidence energy, and a second one is dominated by the width G1 of the lowest resonance. The transition occurs directly from n to 1 without jumps to other intermediate resonant states. This dynamics is discussed in comparison with the (opposite) and well-studied process of quantum decay, with which we find that there are striking similarities in both the exponential and non-exponential regimes. We also analyze the buildup in systems with resonance doublets, where the interference effects produced by the interacting resonances plays an important role. In the latter case we find that the buildup of the probability amplitude exhibits a complex oscillatory behavior that can be characterized by a mix of oscillating contributions with well-defined Rabi type frequencies of the form |E-en|/(h/2p), where en are the nearest resonances around the incidence energy E.