Exact, convergent periodic-orbit expansions of individual energy eigenvalues of regular quantum graphs

Details Exact, convergent periodic-orbit expansions of individual energy eigenvalues of regular quantum graphs Exact, convergent periodic-orbit expansions of individual energy eigenvalues of regular quantum graphs

2001-10-17

arxiv.org/abs/quant-ph/0110109v1

Physics

Quantum Physics

25 pages, 5 figures

Scientific paper

10.1103/PhysRevE.65.046222

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.

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