Spectra of regular quantum graphs

Abstract

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.

32 pages, 10 figures

References in corpus (3)

• Classical dynamics on graphs
• Exact trace formulae for a class of one-dimensional ray-splitting systems
• Mathematical Foundations of Regular Quantum Graphs

Cited by in corpus (6)

• Green's function approach for quantum graphs: an overview
• The influence of geometry and topology of quantum graphs on their nonlinear-optical properties
• Irregular Dynamics in a Solvable One-Dimensional Quantum Graph
• Explicit, analytical solution of scaling quantum graphs
• Dressed quantum graphs with optical nonlinearities approaching the fundamental limit
• Scaling and universality in nonlinear optical quantum graphs containing star motifs