Condensed Matter Theory

Abstract:

We demonstrate the diffusion of single poly(ethylene glycol) molecules on surfaces which change from hydrophilic to hydrophobic over a few micrometers. These gradients in surface energy are shown to drive the molecular diffusion in the direction of the hydrophilic component. The polymer diffusion coefficients on these surfaces are measured by fluorescence correlation spectroscopy and are shown to be elevated by more than an order of magnitude compared to surfaces without the surface energy gradient. Along the gradient, the diffusion is asymmetric, with diffusion coefficients approximately 100 times greater in the direction of the gradient than orthogonal to it. This diffusion can be explained by a Stokes-Einstein treatment of the surface-adsorbed polymer.

Abstract:

Molecular dynamics simulation techniques are used to study the process of aggregation of highly charged stiff polyelectrolytes due to the presence of multivalent salt. The dominant kinetic mode of aggregation is found to be the case of one end of one polyelectrolyte meeting others at right angles, and the kinetic pathway to bundle formation is found to be similar to that of flocculation dynamics of colloids as described by Smoluchowski. The aggregation process is found to favor the formation of finite bundles of 10-11 filaments at long times. Comparing the distribution of the cluster sizes with the Smoluchowski formula suggests that the energy barrier for the aggregation process is negligible. Also, the formation of long-lived metastable structures with similarities to the raft-like structures of actin filaments is observed within a range of salt concentration.

Abstract:

Read-Rezayi fractional quantum Hall states are among the prime candidates for realizing non-Abelian anyons which, in principle, can be used for topological quantum computation. We present a prescription for efficiently finding braids which can be used to carry out a universal set of quantum gates on encoded qubits based on anyons of the Read-Rezayi states with k>2, k≠4. This work extends previous results which only applied to the case k=3 (Fibonacci) and clarifies why, in that case, gate constructions are simpler than for a generic Read-Rezayi state. © 2009 The American Physical Society.