# Material dependence of Casimir forces: gradient expansion beyond proximity

### G. Bimonte 1, T. Emig 2, M. Kardar 3

#### Applied Physics Letters 100 (2012) 074110

A widely used method for estimating Casimir interactions [H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)] between gently curved material surfaces at short distances is the proximity force approximation (PFA). While this approximation is asymptotically exact at vanishing separations, quantifying corrections to PFA has been notoriously difficult. Here we use a derivative expansion to compute the leading curvature correction to PFA for metals (gold) and insulators (SiO$_2$) at room temperature. We derive an explicit expression for the amplitude $\hat\theta_1$ of the PFA correction to the force gradient for axially symmetric surfaces. In the non-retarded limit, the corrections to the Casimir free energy are found to scale logarithmically with distance. For gold, $\hat\theta_1$ has an unusually large temperature dependence.

• 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,
Massachusetts Institute of Technology