Condensed Matter Theory

Abstract:

The stochastic dynamics of colloidal particles with surface activity-in the form of catalytic reaction or particle release-and self-phoretic effects are studied analytically. Three different time scales corresponding to inertial effects, solute redistribution, and rotational diffusion are identified and shown to lead to a plethora of different regimes involving inertial, propulsive, anomalous, and diffusive behaviors. For symmetric active colloids, a regime is found where the mean-squared displacement has a superdiffusive t;{3/2} behavior. At the longest time scales, an effective diffusion coefficient is found which has a nonmonotonic dependence on the size of the colloid.

Abstract:

The general theory of electromagnetic--fluctuation--induced interactions in dielectric bodies as formulated by Dzyaloshinskii, Lifshitz, and Pitaevskii is rewritten as a perturbation theory in terms of the spatial contrast in (imaginary) frequency dependent dielectric function. The formulation can be used to calculate the Casimir-Lifshitz forces for dielectric objects of arbitrary geometry, as a perturbative expansion in the dielectric contrast, and could thus complement the existing theories that use perturbation in geometrical features. We find that expansion in dielectric contrast recasts the resulting Lifshitz energy into a sum of the different many-body contributions. The limit of validity and convergence properties of the perturbation theory is discussed using the example of parallel semi-infinite objects for which the exact result is known.

Abstract:

We apply a hybrid molecular dynamics and mesoscopic simulation technique to study the dynamics of two-dimensional colloidal disks in confined geometries. We calculate the velocity autocorrelation functions and observe the predicted t;{-1} long-time hydrodynamic tail that characterizes unconfined fluids, as well as more complex oscillating behavior and negative tails for strongly confined geometries. Because the t;{-1} tail of the velocity autocorrelation function is cut off for longer times in finite systems, the related diffusion coefficient does not diverge but instead depends logarithmically on the overall size of the system. The Langevin equation gives a poor approximation to the velocity autocorrelation function at both short and long times.