Solution of scaling quantum networks

Abstract

We show that all scaling quantum graphs are explicitly integrable, i.e. any one of their spectral eigenvalues $E_n$ is computable analytically, explicitly, and individually for any given $n$. This is surprising, since quantum graphs are excellent models of quantum chaos [see, e.g., T. Kottos and H. Schanz, Physica E {\bf 9}, 523 (2001)].

arXiv comment11 pages, 1 figure

References in corpus (6)

• Periodic-Orbit Theory of Anderson Localization on Graphs
• Explicitly solvable cases of one-dimensional quantum chaos
• Quantum Graphs: A model for Quantum Chaos
• Exact, convergent periodic-orbit expansions of individual energy eigenvalues of regular quantum graphs
• Exact trace formulae for a class of one-dimensional ray-splitting systems
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Cited by in corpus (1)

• Green's function approach for quantum graphs: an overview