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

Abstract

Key words non-Markovian decay, power law decay, bound stateIt 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 TQ 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 TQ 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.

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

“…In anticipation of this result, we will first briefly review in Sec. III A the influence of an isolated virtual bound state on the non-exponential dynamics when it appears near the threshold [31]. The dynamics near the EP2A revealed in Sec.…”

“…In particular, it is argued in Ref. [31] that a virtual bound state appearing near the continuum threshold can have a strong governing influence on the non-exponential dynamics. The non-exponential dynamics in this case can be divided into two characteristic time zones, separated by the time scale ∆ −1 Q where ∆ Q is the energy gap between the virtual bound state energy and the threshold.…”

“…Specifically it is suggested in Ref. [31] that under fairly general circumstances a relatively intermediate time scale (the long time near zone) should appear during which the survival amplitude falls off as t −1/2 and hence the survival probability exhibits a t −1 decay, while for the asymptotic long time far zone the amplitude follows t −3/2 and the survival probability decays as t −3 6 . The latter result for the far zone dynamics is fairly well known in the literature; for example, see Refs.…”

“…The latter result for the far zone dynamics is fairly well known in the literature; for example, see Refs. [6,11,30,31,[89][90][91].…”

Higher-order time-symmetry-breaking phase transition due to meeting of an exceptional point and a Fano resonance

“…(24). One real solution always exists in the first Riemann sheet below the band edge for any value of ε a , which is a persistent bound state (PBS) attributed to the Van Hove singularity [34,36,37], shown by the dashed-dotted curve in Fig.2. The other two solutions in the second Riemann sheet are bifurcated from two real solutions to a complex conjugate pair of solutions at the bifurcation point, ε a = ε c,1 , which are shown by the solid curves.…”