Anomalous decay of a prepared state due to non-Ohmic coupling to the continuum

TL;DR

This paper investigates the decay dynamics of a prepared quantum state coupled to a continuum with non-Ohmic interactions, revealing universal decay times and conditions for exponential versus power-law decay behaviors.

Contribution

It introduces the concept of a universal generalized Wigner time for non-Ohmic couplings and analyzes the conditions leading to different decay regimes, including exponential and power-law.

Findings

Universal generalized Wigner time $t_0$ characterizes decay.

Decay can be a stretched exponential or power-law depending on model details.

Exponential decay is robust only for Ohmic coupling.

Abstract

We study the decay of a prepared state $E_0$ into a continuum {E_k} in the case of non-Ohmic models. This means that the coupling is $|V_{k,0}| \propto |E_k-E_0|^{s-1}$ with $s \ne 1$. We find that irrespective of model details there is a universal generalized Wigner time $t_0$ that characterizes the evolution of the survival probability $P_0(t)$. The generic decay behavior which is implied by rate equation phenomenology is a slowing down stretched exponential, reflecting the gradual resolution of the bandprofile. But depending on non-universal features of the model a power-law decay might take over: it is only for an Ohmic coupling to the continuum that we get a robust exponential decay that is insensitive to the nature of the intra-continuum couplings. The analysis highlights the co-existence of perturbative and non-perturbative features in the dynamics. It turns out that there are special circumstances in which $t_0$ is reflected in the spreading process and not only in the survival probability, contrary to the naive linear response theory expectation.