Condensed Matter Theory

Abstract:

Fluctuation-induced interactions between anisotropic objects immersed in a nematic liquid crystal are shown to depend on the relative orientation of these objects. The resulting long-range "Casimir" torques are explicitly calculated for a simple geometry where elastic effects are absent. Our study generalizes previous discussions restricted to the case of isotropic walls, and leads to new proposals for experimental tests of Casimir forces and torques in nematics.

Abstract:

We calculate the two-, three-, four-, and five-body (state-independent) effective potentials between the centers of mass (c.m.'s) of self-avoiding walk polymers by Monte Carlo simulations. For full overlap, these coarse-grained n-body interactions oscillate in sign as (-1)(n), and decrease in absolute magnitude with increasing n. We find semiquantitative agreement with a scaling theory, and use this to discuss how the coarse-grained free energy converges when expanded to arbitrary order in the many-body potentials. We also derive effective density dependent two-body potentials that exactly reproduce the pair-correlations between the c.m. of the self avoiding walk polymers. The density dependence of these pair potentials can be largely understood from the effects of the density independent three-body potential. Triplet correlations between the c.m. of the polymers are surprisingly well, but not exactly, described by our coarse-grained effective pair potential picture. In fact, we demonstrate that a pair potential cannot simultaneously reproduce the two- and three-body correlations in a system with many-body interactions. However, the deviations that do occur in our system are very small, and can be explained by the direct influence of three-body potentials.

Abstract:

Equilibrium distribution of interacting ionic particles in a charged disordered background is studied using the nonlinear Poisson-Boltzmann equation. For an arbitrarily given realization of the disorder, an exact solution of the equation is obtained in one dimension using a mapping of the nonlinear Poisson-Boltzmann equation to a self-consistent Schrodinger equation. The resulting density profile shows that the ions are delocalized, despite what the equivalent Schrodinger formulation in one dimension would suggest. It is shown that the ions are not distributed so as to locally neutralize the background, presumably due to their mutual interactions.