Wave scattering through classically chaotic cavities in the presence of absorption: An information-theoretic model

We propose an information-theoretic model for the transport of waves throug h a chaotic cavity in the presence of absorption. The entropy of the S-matr ix statistical distribution is maximized, with the constraint [Tr SSdagger] = alpha n: n is the dimensionality of S, and 0 less than or equal to alpha less than or equal to 1, alpha = 0(1) meaning complete (no) absorption. Fo r strong absorption our result agrees with a number of analytical calculati ons already given in the literature. In that limit, the distribution of the individual (angular) transmission and reflection coefficients becomes expo nential (Rayleigh statistics), even for n = 1. For n much greater than 1 Ra yleigh statistics is attained even with no absorption; here, we extend the study to alpha < 1. The model is compared with random-matrix-theory numeric al simulations: it describes the problem very well for strong absorption, b ut fails for moderate and weak absorptions. Thus, in the latter regime, som e important physical constraint is missing in the construction of the model .