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arXiv · 1210.0449

Tunneling resonances in systems without a classical trapping

D. Borisov·P. Exner·A. Golovina
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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.

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D. Borisov, P. Exner, A. Golovina. 2012-10-01. Tunneling resonances in systems without a classical trapping. https://doi.org/10.1063/1.4773098

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