Wave scattering through classically chaotic cavities in the presence of absorption: A maximum-entropy model

We present a maximum-entropy model for the transport of waves through a classically chaotic cavity in the presence of absorption. The entropy of the S-matrix statistical distribution is maximized, with the constraint 〈TrSS^†〉 = αn: n is the dimensionality of S, and 0 ≤ α ≤ 1. For α = 1 the S-matrix distribution concentrates on the unitarity sphere and we have no absorption; for α = 0 the distribution becomes a delta function at the origin and we have complete absorption. For strong absorption our result agrees with a number of analytical calculations already given in the literature. In that limit, the distribution of the individual (angular) transmission and reflection coefficients becomes exponential - Rayleigh statistics - even for n = 1. For n ≫ 1 Rayleigh statistics is attained even with no absorption; here we extend the study to α < 1. The model is compared with random-matrix-theory numerical simulations: it describes the problem very well for strong absorption, but fails for moderate and weak absorptions. The success of the model for strong absorption is understood in the light of a central-limit theorem. For weak absorption, some important physical constraint is missing in the construction of the model.