QUANTUM TRANSPORT IN QUANTUM BILLIARDS: FROM KELVIN THROUGH ARNOLD

Dynamics of billiard balls and its role in physics have received a wide attention since the monumental lecture by Lord Kelvin at the turn of the 19-th century. Billiards can nowadays be created as quantum dots or antidots in the microscopic world, and one can envisage the quantum-mechanical manifestation of chaos of billiard balls. We show two interesting themes bridging between nonlinear dynamics and quantum transport in these mesoscopic billiards: For antidot lattices, the experimentally-observed anomalous fluctuations in the magneto-resistivity are attributed to orbit bifurcations; for 3-dimensional quantum dots, the Arnold diffusion is pointed out to have a possibility to yield the enhanced magnet-resistance beyond the weak localization correction.