STADIUM IN A MAGNETIC-FIELD - TIME-REVERSAL INVARIANCE SYMMETRY-BREAKING AND ENERGY-LEVEL STATISTICS

We investigate the breaking of time-reversal invariance for the energy spectra of nanostructure devices in the ballistic regime, by conducti ng numerical studies on a stadium billiard model described by a tight- binding Hamiltonian. The symmetry breaking is controlled by a uniform magnetic field, and for different sizes of systems a gradual transitio n from GOE behaviour to GUE behaviour is observed. The results confirm the qualitative criterion for the transition, namely that the transit ion field B-c corresponds to one flux quantum passing through the syst em. Furthermore, all the transition curves show universal behaviour wh en plotted against the flux through the system. Our results are in goo d agreement with the predictions of Random Matrix Theory (RMT), even t hough our Hamiltonian leads to matrices with a very different structur e.