Quantum chaos, localization and tunnelling: microwave experiments on modelgeometries

Microwave experiments using two-dimensional billiard geometries are a preci se test of basic issues in quantum chaos, localization and tunnelling. In c losed chaotic geometries, analysis of eigenvalue statistics yields good agr eement with random-matrix theory. A unique aspect of the experiments is the ability to measure eigenfunctions directly. The influence of periodic orbi t scarring in chaotic eigenfunctions is directly demonstrated. Disordered m icrowave billiards are a textbook model system for studying the quantum pro perties of a single particle in a disordered potential. Localization is dir ectly observed in eigenfunctions of the disordered billiards. Statistical p roperties of disordered eigenfunctions deviate from universal behaviour due to localization. These statistical properties are in good agreement with p redictions from nonlinear-sigma models, although many challenges for furthe r theoretical understanding remain. The experiments can also probe open sys tems, in terms of the quantum resonances and escape rate of a fractal repel ler.