Magnetotransport fluctuations in regular semiconductor ballistic quantum dots

We present studies of the quantum-mechanical transport and the classical billiard transport through ballistic semiconductor quantum dots, where the transport is nonergodic or "regular." These are shown to have quite similar behavior if the classical motion is limited to a collimated set of trajectories. These results are shown to agree substantially with experiments performed on actual semiconductor quantum dots. The results suggest that transport in regular semiconductor quantum dots is clearly distinguished from the equivalent transport in ergodic dots. In particular, the fluctuation spectrum is not random, but highly oscillatory and correlated. The correlation functions for these fluctuations show regular and periodic oscillations that contain only a few, often harmonically related, frequencies. This is fully in keeping with the expectations of semiclassical descriptions of the fluctuations in the density of states of such structures.