Decays in Quantum Hierarchical Models

TL;DR

This paper investigates quantum decay dynamics in hierarchical models, revealing phenomena like Dicke and Zeno effects, and explores how randomness and bandwidth influence decay behavior and fluctuations.

Contribution

It introduces a detailed analysis of decay processes in hierarchical quantum models, highlighting the effects of randomness and bandwidth on decay patterns and fluctuations.

Findings

Decay via a single state involves Dicke and Zeno effects.

Random matrix elements lead to weakly damped oscillations and mesoscopic fluctuations.

Fluctuation amplitude inversely proportional to the square root of the pseudo continuum volume.

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.