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Explicitly solvable cases of one-dimensional quantum chaos

R. Blümel·Yu. Dabaghian·R. V. Jensen
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Abstract

We identify a set of quantum graphs with unique and precisely defined spectral properties called {\it regular quantum graphs}. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are explicitly solvable. The proof is constructive: we present exact periodic orbit expansions for individual energy levels, thus obtaining an analytical solution for the spectrum of regular quantum graphs that is complete, explicit and exact.

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R. Blümel, Yu. Dabaghian, R. V. Jensen. 2001-07-18. Explicitly solvable cases of one-dimensional quantum chaos. https://doi.org/10.1103/physrevlett.88.044101

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