Microwave studies of the spectral statistics in chaotic systems

Abstract

Abstract An overview over the microwave studies of chaotic systems is presented, performed by the authors and their co-workers in Marburg and Nice. In an historical overview the impact of Fritz Haake in particular in the beginning of the experiments is recognized. In the following sections two subjects are presented he was particularly interested in. One of them is the Bohigas–Giannoni–Schmit conjecture stating that the universal features of the spectra of chaotic systems are well described by random matrix theory. Microwave realizations of seven of the ten universal ensembles have been achieved, starting with the Gaussian orthogonal ensemble in the very first experiment, and ending with the chiral ensembles in a recent work. To do the measurements the systems have to be opened by attaching antennas to excite the microwaves. Antennas are theoretically taken into account in terms of a non-Hermitian effective Hamiltonian with an imaginary part taking care of the coupling to the environment. Results on level spacing and widths distribution in open systems are presented as well as on resonance trapping observed when changing the coupling to the environment.