Decays in Quantum Hierarchical Models
Abstract
We study the dynamics of a simple model for quantum decay, where a single state is coupled to a set of discrete states, the pseudo continuum, each coupled to a real continuum of states. We find that for constant matrix elements between the single state and the pseudo continuum the decay occurs via one state in a certain region of the parameters, involving the Dicke and quantum Zeno effects. When the matrix elements are random several cases are identified. For a pseudo continuum with small bandwidth there are weakly damped oscillations in the probability to be in the initial single state. For intermediate bandwidth one finds mesoscopic fluctuations in the probability with amplitude inversely proportional to the square root of the volume of the pseudo continuum space. They last for a long time compared to the non-random case.
Cite
@article{arxiv.0710.1403,
title = {Decays in Quantum Hierarchical Models},
author = {Ariel Amir and Yuval Oreg and Yoseph Imry},
journal= {arXiv preprint arXiv:0710.1403},
year = {2009}
}