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Diffractive systems are quantum-mechanical models with point-likesingularities where usual semiclassical approximation breaks down. An overviewof recent investigations of such systems is presented. The following examplesare considered in details: (i) billiards (both integrable and chaotic) withsmall-size scatterers, (ii) pseudo-integrable polygonal plane billiards, and(iii) billiards with the Bohr-Aharonov flux lines. First, the diffractive traceformulas are discussed with particular emphasis on models where the diffractivecoefficient diverges in certain directions. Second, it is demonstrated that thespectral statistics of diffractive models are different from the statistics ofboth integrable and chaotic systems. The main part of the paper is devoted toanalytical calculations of spectral statistics for certain diffractive models.

Trace Formulas and Spectral Statistics of Diffractive Systems