512 research outputs found
Combinatorial identities for binary necklaces from exact ray-splitting trace formulae
Based on an exact trace formula for a one-dimensional ray-splitting system,
we derive novel combinatorial identities for cyclic binary sequences (P\'olya
necklaces).Comment: 15 page
Exact, convergent periodic-orbit expansions of individual energy eigenvalues of regular quantum graphs
We present exact, explicit, convergent periodic-orbit expansions for
individual energy levels of regular quantum graphs. One simple application is
the energy levels of a particle in a piecewise constant potential. Since the
classical ray trajectories (including ray splitting) in such systems are
strongly chaotic, this result provides the first explicit quantization of a
classically chaotic system.Comment: 25 pages, 5 figure
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