'Persistent currents' and eigenfunctions in microwave resonators with broken time-reversal symmetry

A magnetic flux through a mesoscopic metallic ring gives rise to a persistent current which can be detected via characteristic oscillations of the magnetization depending on the applied field (Levy et al 1990 Phys. Rev. Lett. 64 2074). In this paper a direct visualization of such persistent currents in a microwave analogue experiment is reported, making use of the analogy between the probability density current in the quantum-mechanical system and the Poynting vector in the corresponding electromagnetic one. To break time-reversal symmetry, a small ring of a ferrite material in a static external magnetic field was introduced into the resonator. In our analysis of the experimental data we employ the off-diagonal elements of the scattering matrix., Due to the small size of the ferrite compared to the resonator size the symmetry was partially broken in the sense that the real and the imaginary parts of the wavefunctions are not equally large on average. The statistical properties of the wavefunction's real and imaginary parts Re(psi), Im(psi), respectively, as well as the distributions of the total wavefunction's amplitudes \psi\ and the statistical properties of the probability density currents were also examined and compared to the theoretical predictions.