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.

arXiv commentMinor changes, version to appear in Phys. Rev. A

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Cited by in corpus (19)

• 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
• Proximity force approximation and specular reflection: Application of the WKB limit of Mie scattering to the Casimir effect
• Casimir-Polder interaction for gently curved surfaces
• Beyond-PFA Casimir Force between two spheres at finite temperature
• The role of diffraction in the Casimir effect beyond the proximity force approximation
• Plane-wave approach to the exact van der Waals interaction between colloid particles
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• Casimir Free Energy at High Temperatures: Grounded vs Isolated Conductors
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• On the Derivative Expansion for the Electromagnetic Casimir Free Energy at High Temperatures
• Casimir energy due to inhomogeneous thin plates
• Casimir Interaction Between a Plane and a Sphere: Correction to the Proximity-Force Approximation at Intermediate Temperatures
• 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
• Casimir effect between spherical objects: proximity-force approximation and beyond using plane waves
• 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