Lecture Thorsten Emig

Abstract

According to quantum mechanics, all space is filled with electromagnetic vibrations, even at ultracold temperatures. Two parallel uncharged metal plates limit the number of vibrations between them, creating an effective inward pressure that pushes the plates together -- known as Casimir effect. But the most challenging aspect of this effect is its dependence on geometry. Due to its topological nature, Casimir forces can be controlled by tailoring the shapes of the interacting bodies. However, due to the diffraction of vibrations and the non-additivity of fluctuation induced interactions, there is no intuitive way to tell how the force will change with the object's shape. Recently, there was a resurgence of experiments on Casimir forces, showing also their profound effect on micro- and nanostructures.

In this talk, I shall present a brief introduction to Casimir forces, and a new approach to study the geometry dependence of this interaction. A novel trace formula is presented which yields the relevant information of the spectrum of the Helmholtz wave equation in arbitrary geometries. Perturbative and numerical implementations of this formula yield new and unexpected forms for the Casimir interaction in rather simple geometries. Implications on the non-linear dynamics of nanomechanical systems and actuation schemes will be presented. Our results may lead to the engineering of nano machines in which the geometry dependence of the Casimir force is used to tailor their function.