Fluctuation-induced forces between manifolds immersed in correlated fluids

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Abstract
We develop a general field-theoretical approach for computing fluctuation-induced forces between manifolds immersed in a correlated fluid. Both isotropic, e.g., a superfluid or critical binary mixture, and anisotropic, e.g., nematic or smectic liquid crystals, are considered. The effects of different types of boundary conditions are explored, and in particular the role of deformations from perfect geometries is studied. Specific results include the following: The Casimir force between a flat and a self-affinely rough surface acquires a correction term that decays with the average separation of the plates through an exponent related to the roughness of the boundary. Surface fluctuations in films of correlated fluids may be enhanced, or suppressed by such forces, depending on whether the boundaries are alike or different. We also compute the resulting two-body force between a line (directed polymer) and a surface, and the three-body interaction (repulsive) between three lines.