Casimir forces beyond the proximity approximation

G. Bimonte 1, T. Emig 2, R. L. Jaffe 3, M. Kardar 4

Europhycs Letters 97 (2012) 50001

The proximity force approximation (PFA) relates the interaction between closely spaced, smoothly curved objects to the force between parallel plates. Precision experiments on Casimir forces necessitate, and spur research on, corrections to the PFA. We use a derivative expansion for gently curved surfaces to derive the leading curvature modifications to the PFA. Our methods apply to any homogeneous and isotropic materials; here we present results for Dirichlet and Neumann boundary conditions and for perfect conductors. A Padé extrapolation constrained by a multipole expansion at large distance and our improved expansion at short distances, provides an accurate expression for the sphere-plate Casimir force at all separations.

  • 1. Istituto Nazionale di Fisica Nucleare, Sezione di Napoli (INFN, Sezione di Napoli),
    INFN
  • 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 3. Department of Physics, Center for Theoretical Physics,
    Massachussetts Institute of Technology (MIT)
  • 4. Department of Physics,
    Massachusetts Institute of Technology