Denis Borisov, Pavel Exner, Anastasia Golovina
Tunneling resonances in systems without a classical trapping
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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 $\ell_\pm o\infty$, and derive the leading term in the corresponding asymptotic expansion.