Condensed Matter Theory

Abstract:

A path-integral formulation is used to study the fluctuation-induced interactions between manifolds of arbitrary shape at large separations. It is shown that the form of the interactions crucially depends on the choice of the boundary condition. In particular, whether or not the Casimir interaction is pairwise additive is shown to depend on whether the "metallic" boundary condition corresponds to a "grounded" or an "isolated" manifold.

Abstract:

The statistical mechanics of a ribbon polymer made up of two semiflexible chains is studied using both analytical techniques and simulation. The system is found to have a crossover transition at some finite temperature, from one type of short-range order to a fundamentally different sort of short-range order. In the high temperature regime, the two-point correlation functions of the object are identical to wormlike chains, while in the low temperature regime they are different due to a twist structure. The crossover happens when the persistence length of individual strands becomes comparable to the thickness of the ribbon. In the low temperature regime, the ribbon is observed to have a "kink-rod" structure with a mutual exclusion of twist and bend in contrast to smooth wormlike chain behavior. This is due to its anisotropic rigidity and corresponds to an infinitely strong twist-bend coupling. The double-stranded polymer is also studied in a confined geometry. It is shown that when the polymer is restricted in a particular direction to a size less than the bare persistence length of the individual strands, it develops zigzag conformations which are indicated by an oscillatory tangent-tangent correlation function in the direction of confinement. Increasing the separation of the confining plates leads to a crossover to the free behavior, which takes place at separations close to the bare persistence length. These results are expected to be relevant for experiments that involve complexation of two or more stiff or semiflexible polymers.