Spectra of regular quantum graphs

Details Spectra of regular quantum graphs Spectra of regular quantum graphs

2001-12-18

arxiv.org/abs/quant-ph/0112098v1

Physics

Quantum Physics

32 pages, 10 figures

Scientific paper

10.1134/1.1493174

We consider a class of simple quasi one-dimensional classically non-integrable systems which capture the essence of the periodic orbit structure of general hyperbolic nonintegrable dynamical systems. Their behavior is simple enough to allow a detailed investigation of both classical and quantum regimes. Despite their classical chaoticity, these systems exhibit a ``nonintegrable analog'' of the Einstein-Brillouin-Keller quantization formula which provides their spectra explicitly, state by state, by means of convergent periodic orbit expansions.

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