Dynamical tunneling in mushroom billiards

TL;DR

This paper investigates dynamical tunneling in mushroom billiards through experimental microwave spectra, numerical eigenvalue analysis, and analytical predictions, achieving agreement without free parameters.

Contribution

It introduces an extended analytical approach for predicting tunneling rates in billiards that matches experimental and numerical results without free parameters.

Findings

Experimental microwave spectra confirm tunneling rates.

Numerical eigenvalues yield precise tunneling rates.

Analytical predictions align with experimental and numerical data.

Abstract

We study the fundamental question of dynamical tunneling in generic two-dimensional Hamiltonian systems by considering regular-to-chaotic tunneling rates. Experimentally, we use microwave spectra to investigate a mushroom billiard with adjustable foot height. Numerically, we obtain tunneling rates from high precision eigenvalues using the improved method of particular solutions. Analytically, a prediction is given by extending an approach using a fictitious integrable system to billiards. In contrast to previous approaches for billiards, we find agreement with experimental and numerical data without any free parameter.