Resonances from perturbations of quantum graphs with rationally related edges

Abstract

We discuss quantum graphs consisting of a compact part and semiinfinite leads. Such a system may have embedded eigenvalues if some edge lengths in the compact part are rationally related. If such a relation is perturbed these eigenvalues may turn into resonances; we analyze this effect both generally and in simple examples.

LaTeX source file with 10 pdf figures, 24 pages; a replaced version with minor improvements, to appear in J. Phys. A: Math. Theor

References in corpus (1)

• Approximations of singular vertex couplings in quantum graphs

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