Eur. Phys. J. E (2007) 23: 275-279
https://doi.org/10.1140/epje/i2007-10211-7

Regular Article

The boundary element approach to Van der Waals interactions

¹ Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
² Center for Applied Mathematics and Theoretical Physics, University of Maribor, Maribor, Slovenia
³ Department of Theoretical Physics, J. Stefan Institute, Ljubljana, Slovenia
⁴ LPSB/NICHD, National Institutes of Health, 20892-0924, Bethesda, MD, USA

^* e-mail: gregor.veble@fmf.uni-lj.si
^** e-mail: rudolf.podgornik@fmf.uni-lj.si

Received: 19 March 2007
Accepted: 4 June 2007
Published online: 24 July 2007

Abstract

We develop a boundary element method to calculate Van der Waals interactions for systems composed of domains of spatially constant dielectric response of a general boundary shape. We achieve this by rewriting the interaction energy expression presented in Phys. Rev. B, 62 (2000) 6997 exclusively in terms of surface integrals of surface operators. We validate this approach in the Lifshitz case and give numerical results for the interaction of two spheres as well as the van der Waals self-interaction of a uniaxial ellipsoid. Our method is simple to implement and is particularly suitable for a full, non-perturbative numerical evaluation of non-retarded van der Waals interactions between objects of a completely general shape.