  In this letter, we demonstrate that a non-Hermitian Random Matrix description
can account for both spectral and spatial statistics of resonance states in a
weakly open chaotic wave system with continuously distributed losses. More
specifically, the statistics of resonance states in an open 2D chaotic
microwave cavity are investigated by solving the Maxwell equations with lossy
boundaries subject to Ohmic dissipation. We successfully compare the statistics
of its complex-valued resonance states and associated widths with analytical
predictions based on a non-Hermitian effective Hamiltonian model defined by a
finite number of fictitious open channels.
