Bound states and scattering in quantum waveguides coupled laterally through a boundary window

TL;DR

This paper investigates bound states and scattering phenomena in coupled quantum waveguides with a boundary window, revealing at least one bound state for any window size and analyzing their properties and dynamics.

Contribution

It introduces a numerical analysis of bound states and scattering in coupled waveguides with a boundary window, highlighting their behavior and non-chaotic nature.

Findings

At least one bound state exists for any window size.

Eigenvalues and eigenfunctions are numerically characterized.

The system exhibits non-chaotic spectral statistics.

Abstract

We consider a pair of parallel straight quantum waveguides coupled laterally through a window of a width $ \ell $ in the common boundary. We show that such a system has at least one bound state for any $ \ell>0 $. We find the corresponding eigenvalues and eigenfunctions numerically using the mode--matching method, and discuss their behavior in several situations. We also discuss the scattering problem in this setup, in particular, the turbulent behavior of the probability flow associated with resonances. The level and phase--shift spacing statistics shows that in distinction to closed pseudo--integrable billiards, the present system is essentially non--chaotic. Finally, we illustrate time evolution of wave packets in the present model.