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

Pramana

Pier A Mello¹  Eugene Kogan² 

[1] Instituto de Física, Universidad Nacional Autónoma de México, México D. F., México$$;Department of Physics, Minerva Center and Jack and Pearl Resnick Institute of Advanced Technology, Bar-Ilan University, Ramat-Gan 52900, Israel$$

关键词: Chaotic systems;    wave propagation.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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 $langle {m Tr}SS^{dagger}angle = 𝛼 n: n$ 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.

【 授权许可】

Unknown