PIER A MELLO¹ and EUGENE KOGAN²

¹ Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Mexico D. F., Mexico

² Department of Physics,  Minerva Center and Jack and Pearl Resnick Institute of Advanced Technology, Bar-Ilan University, Ramat-Gan 52900, Israel

Abstract.

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 áTr SS ^†ñ = a n:  n is the dimensionality of S, and 0 £ a £ 1. For a =1 the S-matrix distribution concentrates on the unitarity sphere and we have no absorption; for a =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 a <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.

Keywords:  Chaotic systems; wave propagation..

Pacs Nos.  05.45.+b; 42.25.Bs; 41.20.Jb