Universal statistical aspects of wave scattering by a variety of physical systems ranging from atomic nuclei to mesoscopic systems and microwave cavities are described. A statistical model for the scattering matrix is employed to address the problem of quantum chaotic scattering. The model, introduced in the past in the context of nuclear physics, discusses the problem in terms of a prompt and an equilibrated component: it incorporates the average value of the scattering matrix to account for the prompt processes and satisfies the requirements of flux conservation, causality and ergodicity. The main application of the model is the analysis of electronic transport through ballistic mesoscopic cavities: it describes well the results from the numerical solutions of the Schrödinger equation for two-dimensional cavities.

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-matrixtheory 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.