Negative Magnetoresistance in Three-Dimensional Quantum Billiards: Role of Arnold Diffusion

We bridge between nonlinear dynamics and quantum transport in three-dimensional (3D) quantum dots, by investigating the semiclassical conductance for open 3D ballistic billiards. For partially or completely broken-ergodic 3D billiards such as SO(2) symmetric billiards, the dependence of the conductance on the Fermi wave number is dramatically changed by the lead orientation. In the case of the vertical lead orientation, application of the symmetry-breaking weak magnetic field to such billiards brings about the Arnold diffusion that cannot be seen in 2D billiards. In contrast to the 2D case, the enhanced negative magnetoresistance near the zero field occurs due to the classical Arnold diffusion in addition to a possible quantal weak localization correction.