Numerical methods for fluctuation driven interactions between dielectrics

S. Pasquali, F. Nitti, A. C. Maggs

Published 2007-03-08, updated 2007-08-30Version 2

We develop a discretized theory of thermal Casimir interactions to numerically calculate the interactions between fluctuating dielectrics. From a constrained partition function we derive a surface free energy, while handling divergences that depend on system size and discretization. We derive analytic results for parallel plate geometry in order to check the convergence of the numerical methods. We use the method to calculate vertical and lateral Casimir forces for a set of grooves.