Scale Anomaly and Quantum Chaos in the Billiards with Pointlike Scatterers

TL;DR

This paper links the spectral properties of pseudointegrable billiards with pointlike scatterers to quantum scale invariance violation, showing how the running coupling constant influences level statistics, thus connecting quantum chaos and scale anomaly.

Contribution

It demonstrates that the energy spectra in pseudointegrable billiards are related to quantum scale invariance violation and explains their level statistics through the behavior of the running coupling constant.

Findings

Spectral statistics resemble random matrix theory.

Quantum scale invariance violation affects level distributions.

Running coupling constant behavior explains spectral features.

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.