TY - JOUR

T1 - Wave scattering through classically chaotic cavities in the presence of absorption

T2 - A maximum-entropy model

AU - Mello, Pier A.

AU - Kogan, Eugene

PY - 2002/2

Y1 - 2002/2

N2 - 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.

AB - 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.

KW - Chaotic systems

KW - Wave propagation

UR - http://www.scopus.com/inward/record.url?scp=0036465349&partnerID=8YFLogxK

U2 - 10.1007/s12043-002-0017-x

DO - 10.1007/s12043-002-0017-x

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AN - SCOPUS:0036465349

SN - 0304-4289

VL - 58

SP - 325

EP - 331

JO - Pramana - Journal of Physics

JF - Pramana - Journal of Physics

IS - 2

ER -