Condensed Matter Theory

Abstract:

We examine the effect of Landau level mixing on the braiding statistics of quasiparticles of Abelian and non-Abelian quantum Hall states. While path dependent geometric phases can perturb the Abelian part of the statistics, we find that the non-Abelian properties remain unchanged to an accuracy that is exponentially small in the distance between quasiparticles.

Abstract:

The simple model of a low Reynolds number swimmer made from three spheres that are connected by two arms is considered in its general form and analyzed. The swimming velocity, force-velocity response, power consumption, and efficiency of the swimmer are calculated both for general deformations and also for specific model prescriptions. The role of noise and coherence in the stroke cycle is also discussed.

Abstract:

The coupling between corrugated surfaces due to the lateral Casimir force is employed to propose a nanoscale mechanical device composed of two racks and a pinion. The noncontact nature of the interaction allows for the system to be made frustrated by choosing the two racks to move in the same direction and forcing the pinion to choose between two opposite directions. This leads to a rich and sensitive phase behavior, which makes the device potentially useful as a mechanical {\em sensor} or {\em amplifier}. The device could also be used to make a mechanical {\em clock} signal of tunable frequency.