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

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    • Keywords

       

      Chaotic systems; wave propagation

    • 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 〈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.

    • Author Affiliations

       

      Pier A Mello1 Eugene Kogan2

      1. Instituto de Fisica, Universidad Nacional Autónoma de México, México D. F., México
      2. Department of Physics, Minerva Center and Jack and Pearl Resnick Institute of Advanced Technology, Bar-Ilan University, Ramat-Gan - 52900, Israel
    • Dates

       
  • Pramana – Journal of Physics | News

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