Global versus local billiard level dynamics: The limits of universality

TL;DR

This paper compares global and local level dynamics in billiard systems, showing that universal behaviors depend on whether the system's parameters are changed globally or locally, with different universal correlations observed.

Contribution

It demonstrates the limits of universality in billiard level dynamics by contrasting global and local parameter variations and their effects on universal correlations.

Findings

Global changes follow universal functions by Simons and Altshuler

Local changes exhibit different universal correlations

Chaotic wave functions can be modeled as superpositions of plane waves

Abstract

Level dynamics measurements have been performed in a Sinai microwave billiard as a function of a single length, as well as in rectangular billiards with randomly distributed disks as a function of the position of one disk. In the first case the field distribution is changed globally, and velocity distributions and autocorrelation functions are well described by universal functions derived by Simons and Altshuler. In the second case the field distribution is changed locally. Here another type of universal correlations is observed. It can be derived under the assumption that chaotic wave functions may be described by a random superposition of plane waves.