Marko Robnik(1) and Hans-Jürgen Stöckmann(2)

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
,
, respectively, as well as the distributions of the total
wave function's amplitudes 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*