The derivative expansion approach to the interaction between close surfaces

Abstract

The derivative expansion approach to the calculation of the interaction between two surfaces, is a generalization of the proximity force approximation, a technique of widespread use in different areas of physics. The derivative expansion has so far been applied to seemingly unrelated problems in different areas; it is our principal aim here to present the approach in its full generality. To that end, we introduce an unified setting, which is independent of any particular application, provide a formal derivation of the derivative expansion in that general setting, and study some its properties. With a view on the possible application of the derivative expansion to other areas, like nuclear and colloidal physics, we also discuss the relation between the derivative expansion and some time-honoured uncontrolled approximations used in those contexts. By putting them under similar terms as the derivative expansion, we believe that the path is open to the calculation of next to leading order corrections also for those contexts. We also review some results obtained within the derivative expansion, by applying it to different concrete examples and highlighting some important points.

Minor changes, version to appear in Phys. Rev. A

References in corpus (5)

• The Casimir effect for a sphere and a cylinder in front of plane and corrections to the proximity force theorem
• Casimir interaction between plane and spherical metallic surfaces
• Application of the proximity force approximation to gravitational and Yukawa-type forces
• Numerical evaluation of the Casimir interaction between cylinders
• Classical Casimir interaction in the plane-sphere geometry

Cited by in corpus (11)

• Measurement of the Casimir Force between 0.2 and 8 mum: Experimental Procedures and Comparison with Theory
• Plasma vs Drude modelling of the Casimir force: beyond the proximity force approximation
• Casimir-Polder interaction for gently curved surfaces
• Plane-wave approach to the exact van der Waals interaction between colloid particles
• Critical and near critical phase behaviour and interplay between the thermodynamic Casimir and van der Waals forces in confined non-polar fluid medium with competing surface and substrate potentials
• Casimir energy due to inhomogeneous thin plates
• Finite temperature Casimir interaction between spheres in $(D+1)$-dimensional spacetime: Exact computations and asymptotic expansions
• Derivative expansion for the electromagnetic and Neumann Casimir effects in $2+1$ dimensions with imperfect mirrors
• Wave-scattering from a gently curved surface
• The effect of concurrent geometry and roughness in interacting surfaces
• On the Casimir interaction between two smoothly deformed cylindrical surfaces