Level dynamics in pseudointegrable billiards: an experimental study

TL;DR

This experimental study investigates the spectral level dynamics of pseudointegrable billiards using microwave cavities, revealing Gaussian eigenvalue velocity distributions at high energies and a transition in curvature behavior with increasing genus number.

Contribution

It provides the first experimental analysis of level dynamics in pseudointegrable systems, highlighting how spectral properties evolve with system complexity.

Findings

Eigenvalue velocity distribution is Gaussian at high energies.

Curvature distribution decays as |k|^{-3} for large k.

Intermediate behavior observed for small k, indicating a transition from integrable to chaotic dynamics.

Abstract

The level dynamics of pseudointegrable systems with different genus numbers $g$ is studied experimentally using microwave cavities. For higher energies the distribution of the eigenvalue velocities is Gaussian, as it is expected for chaotic systems with time-reversal symmetry, and shows no dependence on $g$. Also the curvature distribution $P(k)$ for large $k$ is decaying as it is expected for chaotic systems, i.e. $P(k) \sim |k|^{-3}$. For small $k$ an intermediate behavior is found, where $P(k)$ changes from integrable towards chaotic behavior with growing $g$.