Explicitly solvable cases of one-dimensional quantum chaos
arXiv:quant-ph/0107092 · doi:10.1103/PhysRevLett.88.044101
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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