Quantum chaos, localization and tunnelling: Microwave experiments on model geometries

Abstract

Microwave experiments using two-dimensional billiard geometries are a precise test of basic issues in quantum chaos, localization and tunnelling. In closed chaotic geometries, analysis of eigenvalue statistics yields good agreement with random-matrix theory. A unique aspect of the experiments is the ability to measure eigenfunctions directly. The influence of periodic orbit scarring in chaotic eigenfunctions is directly demonstrated. Disordered microwave billiards are a textbook model system for studying the quantum properties of a single particle in a disordered potential. Localization is directly observed in eigenfunctions of the disordered billiards. Statistical properties of disordered eigenfunctions deviate from universal behaviour due to localization. These statistical properties are in good agreement with predictions from nonlinear-sigma models, although many challenges for further theoretical understanding remain. The experiments can also probe open systems, in terms of the quantum resonances and escape rate of a fractal repeller.