Complex Energy Spectrum and Time Evolution of QBIC States in a Two-Channel Quantum wire with an Adatom Impurity

TL;DR

This paper analyzes the complex energy spectrum and long-lived quasi-bound states in a two-channel quantum wire with an adatom impurity, revealing non-perturbative effects due to van Hove singularities and demonstrating the stability of QBIC states.

Contribution

It provides a detailed analysis of QBIC states, including their complex eigenvalues and non-perturbative decay rates, expanding understanding of resonant states in quantum wires.

Findings

QBIC states have decay rates of order g^6.

Van Hove singularities cause non-analytic effects in the spectrum.

Numerical simulations confirm the stability of QBIC states.

Abstract

We provide detailed analysis of the complex energy eigenvalue spectrum for a two-channel quantum wire with an attached adatom impurity. The study is based on our previous work [Phys. Rev. Lett. 99, 210404 (2007)], in which we presented the quasi-bound states in continuum (or QBIC states). These are resonant states with very long lifetimes that form as a result of two overlapping continuous energy bands one of which, at least, has a divergent van Hove singularity at the band edge. We provide analysis of the full energy spectrum for all solutions, including the QBIC states, and obtain an expansion for the complex eigenvalue of the QBIC state. We show that it has a small decay rate of the order $g^6$, where $g$ is the coupling constant. As a result of this expansion, we find that this state is a non-analytic effect resulting from the van Hove singularity; it cannot be predicted from the ordinary perturbation analysis that relies on Fermi's golden rule. We will also numerically demonstrate the time evolution of the QBIC state using the effective potential method in order to show the stability of the QBIC wave function in comparison with that of the other eigenstates.