Amplification of non-Markovian decay due to bound state absorption into continuum

TL;DR

This paper investigates how the decay behavior of quantum systems changes when a bound state approaches the continuum threshold, revealing two distinct power law decay regimes and their dependence on system parameters.

Contribution

It identifies two different long-time power law decay regimes in non-Markovian quantum decay and relates the transition timescale to the bound state's proximity to the continuum threshold.

Findings

Near zone decay follows t^{-1} law

Far zone decay follows t^{-3} law

Transition timescale diverges as bound state approaches continuum

Abstract

It is known that quantum systems yield non-exponential (power law) decay on long time scales, associated with continuum threshold effects contributing to the survival probability for a prepared initial state. For an open quantum system consisting of a discrete state coupled to continuum, we study the case in which a discrete bound state of the full Hamiltonian approaches the energy continuum as the system parameters are varied. We find in this case that at least two regions exist yielding qualitatively different power law decay behaviors; we term these the long time `near zone' and long time `far zone.' In the near zone the survival probability falls off according to a $t^{-1}$ power law, and in the far zone it falls off as $t^{-3}$. We show that the timescale $T_Q$ separating these two regions is inversely related to the gap between the discrete bound state energy and the continuum threshold. In the case that the bound state is absorbed into the continuum and vanishes, then the time scale $T_Q$ diverges and the survival probability follows the $t^{-1}$ power law even on asymptotic scales. Conversely, one could study the case of an anti-bound state approaching the threshold before being ejected from the continuum to form a bound state. Again the $t^{-1}$ power law dominates precisely at the point of ejection.