Scale Anomaly and Quantum Chaos in the Billiards with Pointlike Scatterers

Abstract

We argue that the random-matrix like energy spectra found in pseudointegrable billiards with pointlike scatterers are related to the quantum violation of scale invariance of classical analogue system. It is shown that the behavior of the running coupling constant explains the key characteristics of the level statistics of pseudointegrable billiards.

10 pages, RevTex file, uuencoded

References in corpus (3)

• Diffractive orbits in quantum billiards
• Periodic Orbit Quantization beyond Semiclassics
• Wave Chaos in Quantum Billiards with Small but Finite-Size Scatterer

Cited by in corpus (9)

• Spectral Statistics of Rectangular Billiards with Localized Perturbations
• Singular statistics revised
• Long-range correlations in rectangular cavities containing point-like perturbations
• Spectral Properties of Three-Dimensional Quantum Billiards with a Pointlike Scatterer
• Level statistics and eigenfunctions of pseudointegrable systems: dependence on energy and genus number
• Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards
• Exploring integrability-chaos transition with a sequence of independent perturbations
• Persistent currents due to point obstacles
• Quantum chaos in a harmonic waveguide with scatterers