Two-dimensional thermal radiation in disk-like resonators

In disk-like resonators where the size in one direction is small in comparison to the sizes in the two perpendicular directions, the range of low frequencies corresponds to a two-dimensional mode structure with a two-dimensional mode density that is explicitly discussed for a rectangular resonator. This leads to a two-dimensional black-body radiation law if the temperature correlated with resonator size are small enough to occupy only these modes according to Bose-Einstein statistics and if there is a lot of two-dimensional modes within the new radiation contour to justify the two-dimensional continuum approximation. We discuss the conditions for this case and the corresponding laws for energy and entropy and for the radiation pressure which is a negative pressure onto the plates. The Casimir effect which remains for the absolute temperature equal to zero and which has also a negative value is the residual effect from the difference of the zero-point energies of the resonator configuration in comparison to the free space and is shortly discussed. (author)