Abstract： Two statistical properties, the nearest neighbor energy level spacing distribution P( s ) and the spectral rigidity Δ3( L ), are reported for energy level of a quantum well in a tilted magnetic field. Time-reversal ( T ) symmetry is broken in the system. The system is invariant under the anti-unitary combination of symmetric operations which include T, leading to what is called false T-violation. With the increasing magnetic field, P(s) and Δ3( L ) change from Brody type-like distribution to the Gaussian orthogonal ensemble (GOE) distribution. This result is a clear manifestation of quantum chaos in the system and is in agreement with the prediction of which the false T-violation suffices to give the energy spectra the properties of the GOE, instead of the Gaussian unitary ensemble (GUE). The result indicates that the system translates from mixed-type state to quantum chaotic state. However, the spectral rigidity Δ3( L ) turns into GUE with the magnetic field increasing. The different demonstration of P( s ) and the Δ3(L) is due to the counting of only finite semi-classical orbits.
LIU Bo;DAI Jian-hua;ZHANG Guang-cai;ZHANG Hong-jun. Manifestation of Quantum Chaos in the Spectra of Quantum Well with Tilted Magnetic Field[J]. 中国物理快报, 1999, 16(2): 140-142.
LIU Bo, DAI Jian-hua, ZHANG Guang-cai, ZHANG Hong-jun. Manifestation of Quantum Chaos in the Spectra of Quantum Well with Tilted Magnetic Field. Chin. Phys. Lett., 1999, 16(2): 140-142.
1999, Vol. 16 
