Time Reversal and Exceptional Points

Eigenvectors of decaying quantum systems are studied at exceptional points of the Hamiltonian. Special attention is paid to the properties of the system under time reversal symmetry breaking. At the exceptional point the chiral character of the system -- found for time reversal symmetry -- generically persists. It is, however, no longer circular but rather elliptic.Comment: submitted for publicatio

The Chirality of Exceptional Points

Exceptional points are singularities of the spectrum and wave functions which occur in connection with level repulsion. They are accessible in experiments using dissipative systems. It is shown that the wave function at an exceptional point is one specific superposition of two wave functions which are themselves specified by the exceptional point. The phase relation of this superposition brings about a chirality which should be detectable in an experiment.Comment: four pages, one postscript figure, to be submitted to PR

Cross-Section Fluctuations in Chaotic Scattering

For the theoretical prediction of cross-section fluctuations in chaotic scattering, the cross-section autocorrelation function is needed. That function is not known analytically. Using experimental data and numerical simulations, we show that an analytical approximation to the cross-section autocorrelation function can be obtained with the help of expressions first derived by Davis and Boose. Given the values of the average S-matrix elements and the mean level density of the scattering system, one can then reliably predict cross-section fluctuations

Chaotic Scattering in the Regime of Weakly Overlapping Resonances

We measure the transmission and reflection amplitudes of microwaves in a resonator coupled to two antennas at room temperature in the regime of weakly overlapping resonances and in a frequency range of 3 to 16 GHz. Below 10.1 GHz the resonator simulates a chaotic quantum system. The distribution of the elements of the scattering matrix S is not Gaussian. The Fourier coefficients of S are used for a best fit of the autocorrelation function if S to a theoretical expression based on random--matrix theory. We find very good agreement below but not above 10.1 GHz