Numerical evaluation of the Casimir interaction between cylinders

F. C. LOMBARDO, F. D. MAZZITELLI, AND P. I. VILLAR

PHYSICAL REVIEW D - PARTICLE AND FILDS

AMERICAN PHYSICAL SOC

Lugar: New York; Año: 2008 vol. 78 p. 850091 - 8500911

0556-2821

   We numerically evaluate the Casimir interaction energy for configurations involving two perfectlyconducting eccentric cylinders and a cylinder in front of a plane. We consider in detail several specialcases. For quasiconcentric cylinders, we analyze the convergence of a perturbative evaluation based onsparse matrices. For concentric cylinders, we obtain analytically the corrections to the proximity forceapproximation up to second order, and we present an improved numerical procedure to evaluate theinteraction energy at very small distances. Finally, we consider the configuration of a cylinder in front of aplane. We first show numerically that, in the appropriate limit, the Casimir energy for this configurationcan be obtained from that of two eccentric cylinders. Then we compute the interaction energy at smalldistances, and compare the numerical results with the analytic predictions for the first order corrections tothe proximity force approximation.