Universal statistics of the local Green’s function in wave chaotic systems with absorption

We establish a general relation between the statistics of the local Green’s function for systems with chaotic wave scattering and uniform energy loss (absorption) and the two-point correlator of its resolvents for the same system without absorption. Within the random matrix approach, this kind of a fluctuation dissipation relation allows us to derive the explicit analytic expression for the joint distribution function of the real and imaginary part of the local Green’s function for all symmetry classes as well as at an arbitrary degree of time-reversal symmetry breaking in the system. The outstanding problem of orthogonal symmetry is further reduced to simple quadratures. The results can be applied, in particular, to the experimentally accessible impedance and reflection in a microwave cavity attached to a single-mode antenna.