Trace Formulas and Spectral Statistics of Diffractive Systems

  • Eugene Bogomolny
Conference paper
Part of the Progress in Mathematics book series (PM, volume 202)


Diffractive systems are quantum-mechanical models with point-like singularities where usual semiclassical approximation breaks down. An overview of recent investigations of such systems is presented. The following examples are considered in detail: (i) billiards (both integrable and chaotic) with small-size scatterers, (ii) pseudo-integrable polygonal plane billiards, and (iii) billiards with the Bohr-Aharonov flux lines. First, the diffractive trace formulas are discussed with particular emphasis on models where the diffractive coefficient diverges in certain directions. Second, it is demonstrated that the spectral statistics of diffractive models are different from the statistics of both integrable and chaotic systems. The main part of the lecture is devoted to analytical calculations of spectral statistics for certain diffractive models.


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© Springer Basel AG 2001

Authors and Affiliations

  • Eugene Bogomolny
    • 1
  1. 1.Laboratoire de Physique Théorique et Modelés StatistiquesUniversité de Paris XIOrsay CedexFrance

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