Thermal Casimir effect with soft boundary conditions

Abstract

We consider the thermal Casimir effect in systems of parallel plates coupled to a mass-less free field theory via quadratic interaction terms which suppress (i) the field on the plates (ii) the gradient of the field in the plane of the plates. These boundary interactions correspond to (i) the presence of an electrolyte in the plates and (ii) a uniform field of dipoles, in the plates, which are polarizable in the plane of the plates. These boundary interactions lead to Robin type boundary conditions in the case where there is no field outside the two plates. In the appropriate limit, in both cases Dirichlet boundary conditions are obtained but we show that in case (i) the Dirichlet limit breaks down at short inter-plate distances and in (ii) it breaks down at large distances. The behavior of the two plate system is also seen to be highly dependent on whether the system is open or closed. In addition we analyze the Casimir force on a third plate placed between two outer plates. The force acting on the central plate is shown to be highly sensitive to whether or not the fluctuating scalar field is present in the region exterior to the two confining plates.

8 pages RevTex, 2 .eps figures

References in corpus (9)

• The `Friction' of Vacuum, and other Fluctuation-Induced Forces
• The Theory of Boundary Critical Phenomena
• Casimir effect for scalar fields under Robin boundary conditions on plates
• Crossover from Attractive to Repulsive Casimir Forces and Vice Versa
• Casimir effect for the scalar field under Robin boundary conditions: A functional integral approach
• Electrostatic Fluctuations in Soap Films
• Casimir force between planes as a boundary finite size effect
• Path integrals for stiff polymers applied to membrane physics
• The thermal Casimir effect in lipid bilayer tubules

Cited by in corpus (8)

• Critical Casimir forces and adsorption profiles in the presence of a chemically structured substrate
• The out of equilibrium behavior of Casimir type fluctuation induced forces for free classical fields
• Relaxation of the thermal Casimir force between net neutral plates containing Brownian charges
• Finite temperature Casimir effect for scalar field with Robin boundary conditions in spacetime with extra dimensions
• Resonant alteration of propagation in guiding structures with complex Robin parameter and its magnetic-field-induced restoration
• Excluded volume effects in macromolecular forces and ion-interface interactions
• Pseudo-Casimir stresses and elasticity of a confined elastomer film
• Explicit Solvent Effects on Macromolecular Interactions From a Solvent-Augmented Contact Value Theorem