Tunneling resonances in systems without a classical trapping

Abstract

In this paper we analyze a free quantum particle in a straight Dirichlet waveguide which has at its axis two Dirichlet barriers of lengths ${\ell }_{\pm }$ separated by a window of length 2a. It is known that if the barriers are semiinfinite, i.e. we have two adjacent waveguides coupled laterally through the boundary window, the system has for any a>0 a finite number of eigenvalues below the essential spectrum threshold. Here we demonstrate that for large but finite ${\ell }_{\pm }$ the system has resonances which converge to the said eigenvalues as ${\ell }_{\pm }\to \infty$, and derive the leading term in the corresponding asymptotic expansion.

References in corpus (4)

• Asymptotic behaviour of the spectrum of a waveguide with distant perturbations
• Distant perturbations of the Laplacian in a multi-dimensional space
• Planar waveguide with "twisted" boundary conditions: small width
• Discrete spectrum of a pair of nonsymmetric waveguides coupled by a window

Cited by in corpus (4)

• Eigenvalue inequalities and absence of threshold resonances for waveguide junctions
• Spacing gain and absorption in a simple $\mathcal{P}\mathcal{T}$-symmetric model: spectral singularities and ladders of eigenvalues and resonances
• Defect resonances of truncated crystal structures
• Straight quantum layer with impurities inducing resonances