  The effective Hamiltonian formalism is extended to vectorial electromagnetic
waves in order to describe statistical properties of the field in reverberation
chambers. The latter are commonly used in electromagnetic compatibility tests.
As a first step, the distribution of wave intensities in chaotic systems with
varying opening in the weak coupling limit for scalar quantum waves is derived
by means of random matrix theory. In this limit the only parameters are the
modal overlap and the number of open channels. Using the extended effective
Hamiltonian, we describe the intensity statistics of the vectorial
electromagnetic eigenmodes of lossy reverberation chambers. Finally, the
typical quantity of interest in such chambers, namely, the distribution of the
electromagnetic response, is discussed. By determining the distribution of the
phase rigidity, describing the coupling to the environment, using random matrix
numerical data, we find good agreement between the theoretical prediction and
numerical calculations of the response.
