Condensed Matter Theory

Abstract:

The force experienced by objects embedded in a correlated medium undergoing thermal fluctuations-the so-called fluctuation-induced force-is actually itself a fluctuating quantity. Using a scalar field model, we compute the corresponding probability distribution and show that it is a Gaussian centered on the well-known Casimir force, with a nonuniversal standard deviation that can be typically as large as the mean force itself. The relevance of these results to the experimental measurement of fluctuation-induced forces in soft condensed matter is discussed, as well as the influence of the finite temporal resolution of the measuring apparatus.

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.