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

Marko Vranicar(1), Michael Barth(2), Gregor Veble(1)
Marko Robnik(1) and Hans-Jürgen Stöckmann(2)

(1) CAMTP - Center for Applied Mathematics and Theoretical Physics,
University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia
(2) Fachbereich Physik, Universität Marburg, Renthof 5, D-35032 Marburg, Germany

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 of the applied field [Lévy et al., Phys. Rev. Lett. 64, 2074 (1990)]. 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 wave functions are not equally large on average. The statistical properties of the wave function's real and imaginary parts ${\rm Re}(\psi)$, ${\rm Im}(\psi)$, respectively, as well as the distributions of the total wave function's amplitudes $\vert\psi\vert$ and the statistical properties of the probability density currents were also examined and compared to the theoretical predictions.

References
Lévy L P, Dolan G, Dunsmuir J and Bouchiat H 1990 Phys. Rev. Lett. 64 2074
Saichev A I, Ishio H, Sadreev A F and Berggren K F 2002 J. Phys. A: Math. Gen. 35 L87
Stein J, Stöckmann H-J and Stoffregen U 1995 Phys. Rev. Lett. 75 53
Vranicar M, Barth M, Veble G, Robnik M and Stöckmann H-J 2002 J. Phys. A: Math. Gen. 35 at press