Van der Waals and Casimir Forces: Effects of Finite Temperature and Dissipation

Bo E. Sernelius

Department of Physics and Measurement Technology

Linköping University

SE-581 83 Linköping, Sweden

I will discuss the zero-temperature dispersion-forces in terms of changes in the zero-point energy of the electromagnetic normal-modes of the system. The van der Waals and Casimir forces are due to different types of mode. In the simplest cases the result can be found from summing the changes of each mode. In the more complex situations one may use a generalization of the Argument Principle, a well-known theorem from complex analysis, and end up with integrations or summations along the complex-frequency axis.

I will address the dispersion forces between metal plates and discuss effects from finite temperature and dissipation. Results for "perfect" metals, from simple Drude approximation, from full Drude approximation and from using the experimental dielectric function will be presented.

I will also briefly discuss the analytical properties of the dissipation correction in the dielectric function, the dynamic relaxation time.

At the end I will raise some questions or discussion topics:

The first is about thermal equilibrium. Our system consist of two parts: the interior of the metal plates and the surrounding vacuum. The interior is kept at 300 K. The vacuum in the outer space is kept at 3 K. Can we assume that the vacuum between and near the plates is at equilibrium at 300 K?

Why do the TM-modes but not the TE-modes contribute to the dominating term at high temperatures and/or large separations?

Are the boundary conditions used by us and by others O.K.?