Manifestation of quantum chaos in the spectra of quantum well with tilted magnetic field

Two statistical properties, the nearest neighbor energy level spacing distr ibution P(s) and the spectral rigidity Delta(3)(L), are reported for energy level of a quantum well in a tilted magnetic field. Time-reversal (T) symm etry is broken in the system. The system is invariant under the anti-unitar y combination of symmetric operations which include T, leading to what is c alled false T-violation. With the increasing magnetic field, P(s) and Delta (3)(L) change from Brody type-like distribution to the Gaussian orthogonal ensemble (GOE) distribution. This result is a dear manifestation of quantum chaos in the system and is in agreement with the prediction of which the f alse T-violation suffices to give the energy spectra the properties of the GOE, instead of the Gaussian unitary ensemble (GUE). The result indicates t hat the system translates from mixed-type state to quantum chaotic state. H owever, the spectral rigidity Delta(3) (L) turns into GUE with the magnetic field increasing. The different demonstration of P(s) and the Delta(3)(L) is due to the counting of only finite semi-classical orbits.