Density and Correlation functions of vortex and saddle points in open billiard systems

TL;DR

This study combines microwave experiments and the Random Wave Model to analyze the density and spatial correlations of vortices and saddle points in open billiard systems, providing new experimental insights and theoretical expressions.

Contribution

It introduces an improved experimental setup to measure saddle point correlations and derives new theoretical expressions for their density near boundaries.

Findings

Experimental measurements agree with RWM predictions.

Derived asymptotic correlation functions match experimental data.

Established density expressions for saddle points near boundaries.

Abstract

We present microwave measurements for the density and spatial correlation of current critical points in an open billiard system, and compare them with the predictions of the Random Wave Model (RWM). In particular, due to a novel improvement of the experimental set-up, we determine experimentally the spatial correlation of saddle points of the current field. An asymptotic expression for the vortex-saddle and saddle-saddle correlation functions based on the RWM is derived, with experiment and theory agreeing well. We also derive an expression for the density of saddle points in the presence of a straight boundary with general mixed boundary conditions in the RWM, and compare with experimental measurements of the vortex and saddle density in the vicinity of a straight wall satisfying Dirichlet conditions.