Fluctuations of Casimir forces on finite objects. I. Spheres and hemispheres

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Abstract
The mean-square forces that result from the zero-point fluctuations of quantized fields are calculated when acting on spheres and hemispheres of variable sizes. For the Maxwell field the boundary conditions of a perfectly conducting surface are imposed; the scalar field is investigated for Neumann and Dirichlet boundary conditions. The force is averaged over a finite time T; small and large objects are distinguished on the scale of cT. The results for the sphere and the hemisphere are compared with those for a piston that is embedded in an infinite plane. A small hemisphere and a small piston are found to have fluctuations of the same order of magnitude, while on a small sphere the fluctuations are by two orders of magnitude smaller because of correlations of fluctuations on the two sides of the sphere. Large spheres are shown to fit into the picture of large objects being composed of many patches each with the fluctuations impinging as on a large piston.

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