Condensed Matter Theory

Abstract:

We study the classical hard-core dimer model on the triangular lattice. Following Kasteleyn's fundamental theorem on planar graphs, this problem is soluble using Pfaffians. This model is particularly interesting for, unlike the dimer problems on the bipartite square and hexagonal lattices, its correlations are short ranged with a correlation length of less than one lattice constant. We compute the dimer-dimer and monomer-monomer correlators, and find that the model is deconfining: the monomer-monomer correlator falls off exponentially to a constant value 0.1494..., only slightly below the nearest-neighbor value of 1/6. We also consider the anisotropic triangular lattice model in which the square lattice is perturbed by diagonal bonds of one orientation and small fugacity. We show that the model becomes noncritical immediately and that this perturbation is equivalent to adding a mass term to each of two Majorana fermions that are present in the long wavelength limit of the square lattice problem.

Abstract:

Phase separating binary fluids with the addition of immobile particles, which act as osmotic force centres, were simulated using a Lattice Boltzmann model in two dimensions. In the hydrodynamic over-damped limit, where the flow is entirely driven by capillary effects, the presence of particles that are preferentially wetted by one of the fluid components significantly affects the kinetics of the growth of the fluid domains. The late time dynamics is governed by the wetting interactions and the final size of the domains can be tailored by varying the strength of the particles-fluid interaction as well as the particles concentration. These features are predicted within a simple theoretical model and are amenable of experimental checks.

Abstract:

The Casimir force between macroscopic bodies depends strongly on their shape and orientation. To study this geometry dependence in the case of two deformed metal plates, we use a path integral quantization of the electromagnetic field which properly treats the many-body nature of the interaction, going beyond the commonly used pairwise summation (PWS) of van der Waals forces. For arbitrary deformations we provide an analytical result for the deformation induced change in Casimir energy, which is exact to second order in the deformation amplitude. For the specific case of sinusoidally corrugated plates, we calculate both the normal and the lateral Casimir forces. The deformation induced change in the Casimir interaction of a flat and a corrugated plate shows an interesting crossover as a function of the ratio of the mean platedistance H to the corrugation length \lambda: For \lambda \ll H we find a slower decay \sim H^{-4}, compared to the H^{-5} behavior predicted by PWS which we show to be valid only for \lambda \gg H. The amplitude of the lateral force between two corrugated plates which are out of registry is shown to have a maximum at an optimal wavelength of \lambda \approx 2.5 H. With increasing H/\lambda \gtrsim 0.3 the PWS approach becomes a progressively worse description of the lateral force due to many-body effects. These results may be of relevance for the design and operation of novel microelectromechanical systems (MEMS) and other nanoscale devices.