Quantum tunneling decay due to a resonance state of negative energy and a decaying width

Abstract

By using an exact analytical formalism for quantum tunneling decay we show the existence of a regime of purely nonexponential decay for the survival probability in the full time interval and a propagating probability density along the external interaction region that evolves as a spreading process having no wavefront. This decaying regime follows from a complex pole of the propagator which in the wave number plane possesses an imaginary part larger than the corresponding real part, which implies a negative resonance energy and a decaying width, together with a dominant large overlap of the initial decaying state with the corresponding resonant state of the problem.