Derivative expansion for the electromagnetic and Neumann Casimir effects in $2+1$ dimensions with imperfect mirrors

Abstract

We calculate the Casimir interaction energy in $d=2$ spatial dimensions between two (zero-width) mirrors, one flat, and the other slightly curved, upon which {\em imperfect\/} conductor boundary conditions are imposed for an Electromagnetic (EM) field. Our main result is a second-order Derivative Expansion (DE) approximation for the Casimir energy, which is studied in different interesting limits. In particular, we focus on the emergence of a non-analyticity beyond the leading-order term in the DE, when approaching the limit of perfectly-conducting mirrors. We also show that the system considered is equivalent to a dual one, consisting of a massless real scalar field satisfying imperfect Neumann conditions (on the very same boundaries). Therefore, the results obtained for the EM field hold also true for the scalar field model

References in corpus (6)

• The Casimir effect for a sphere and a cylinder in front of plane and corrections to the proximity force theorem
• Thermal corrections to the Casimir effect
• Casimir-Polder interaction for gently curved surfaces
• The derivative expansion approach to the interaction between close surfaces
• Small distance expansion for radiative heat transfer between curved objects
• Exact classical sphere-plate Casimir interaction in (D+1)-dimensional spacetime