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

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

1995-12-11

arxiv.org/abs/cond-mat/9512088v2

J.Math.Phys. 37 (1996) 4867-4887

Physics

Condensed Matter

LaTeX text file with 12 ps figures

Scientific paper

10.1063/1.531673

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.

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