English

Resonances from perturbations of quantum graphs with rationally related edges

Mathematical Physics 2019-12-10 v2 math.MP Spectral Theory Quantum Physics

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.

Keywords

Cite

@article{arxiv.0912.3936,
  title  = {Resonances from perturbations of quantum graphs with rationally related edges},
  author = {Pavel Exner and Jiri Lipovsky},
  journal= {arXiv preprint arXiv:0912.3936},
  year   = {2019}
}

Comments

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