Berlin 2005 – scientific programme

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DY: Dynamik und Statistische Physik

DY 42: Statistical Physics (General) II

DY 42.3: Talk

Tuesday, March 8, 2005, 14:45–15:00, TU H3010

Casimir forces and Geometry — •Rauno Buescher and Thorsten Emig — Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Koeln, Germany

Casimir interactions between metallic surfaces can now be measured very precisely. However, on the theoretical side there is only little knowledge about Casimir forces in geometries going beyond the simplest cases as two parallel plates or a sphere and a plate. The only available approximations start from an expansion of the force at short distances, leading to the so-called proximity force approximation (PFA). Here we present a novel approach which is based on a numerical implementation of a path integral quantization of the electromagnetic field. It can be applied to surfaces with arbitrarily strong deformations at any distance. More specifically, we consider the normal and lateral force between periodically deformed surfaces. In contrast to the in general complicated behavior at short distances, as described by the PFA, we observe a universal behavior of the force at large distances is the sense that the interaction depends only on the mode with the largest wave length of the surface deformation spectrum and the modulations at smaller scales are irrelevant. Our findings thus complement the PFA approach, and yield even the crossover between the two regimes. We find that the in recent experiments detected lateral force changes with the lateral surface displacement in a way which can be distinct from the change of the surface profile itself. Our results can be extended to finite temperatures.