Electromagnetic field distributions in 3-dimensional irregular cavities
Ulrich Dörr · Hans-Jürgen Stöckmann · Michael Barth · Ulrich Kuhl
The eigenfrequencies νn of the cavity are measured in
dependance of the metallic bead position r:
Wavefunctions and their Δν distribution
|wave functions||distributions of Δν|
Δν distribution of wavefunctions
Distribution P(Δν) is defined by:
If all components of E and B are independently Gaussian distributed, i.e,
Only for chaotic wave functions the ansatz is valid. If the wave function is scarred, deviations from the expected deviations can be seen. Therefore the distribution can be used as a check whether the wave function is chaotic or not.
Δν distribution at the walls
Close to the walls three field components must be zero, due to the boundary conditions. Thus the distribution of Δν must be different and can be calculated by using only three independent components of the fields.
At the walls (d < 10mm) the deviations from the volume distribution (dashed dotted line) clearly can be seen. The sharp peak of the expected distribution (dashed line) can't be resolved.
In the intermediate regime (10mm < d < 20mm) a transition from border to volume distribution is found.
For the data well inside the cavity (d > 20mm) the volume distribution describes the experimental findings.
Spatial correlation functions
(in cooperation with B. Eckhardt)
The spatial correlation function is defined by:
Longitudinal correlation function along the displacement:
Transversal correlation function:
If the polarization is not considered, one expects:
Experimental correlation functions(- - - - including polarization, · · · · excluding polarization)
ResultsThough the electromagnetic fields E and B are coupled by the Maxwell equations, the six components can be considered as independently Gaussian distributed.
==> Field distributions can be described by random superposition of plane waves.