Distribution of the reflection eigenvalues of a weakly absorbing chaotic cavity
C.W.J. Beenakker, P.W. Brouwer
TL;DR
This paper investigates the distribution of reflection eigenvalues in weakly absorbing chaotic cavities, revealing they follow a generalized Laguerre ensemble due to their relation to the time-delay matrix.
Contribution
It establishes a theoretical connection between reflection eigenvalues and the generalized Laguerre ensemble in weakly absorbing chaotic systems.
Findings
Eigenvalues of the scattering matrix product follow a generalized Laguerre distribution.
The relationship between scattering matrix and time-delay matrix is key.
Provides a theoretical framework for understanding absorption effects in chaotic cavities.
Abstract
The scattering-matrix product SS+ of a weakly absorbing medium is related by a unitary transformation to the time-delay matrix without absorption. It follows from this relationship that the eigenvalues of SS+ for a weakly absorbing chaotic cavity are distributed according to a generalized Laguerre ensemble.
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