1997/11/12 by Piet W. Brouwer, P. W. Brouwer · 3 citations
Mathematics · Physics and Astronomy · #Absorption (acoustics) #Condensed matter physics #Conductance #Distribution (mathematics) #Eigenvalues and eigenvectors #Exponential function #Mathematical analysis #Mathematics #Optics #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Random Matrices and Applications #Random matrix #Spectral Theory in Mathematical Physics #Telecommunications #Transmission (telecommunications) #Transmittance #Waveguide #cond-mat.dis-nn #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.57.10526
published as Phys. Rev. B 57, 10526 (1998) · 13 pages, RevTeX; 9 figures included
arxiv created 1997/11/12 · openalex publication_date 1998/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We compute the statistical distribution of the transmittance of a random waveguide with absorption in the limit of many propagating channels. We consider the average and fluctuations of the conductance T=trt^\ifmmode†\else\textdagger\fit, where t is the transmission matrix, the density of transmission eigenvalues \ensuremathτ (the eigenvalues of t^\ifmmode†\else\textdagger\fit), and the distribution of the plane-wave transmittances Ta and Tab. For weak absorption (length L smaller than the exponential absorption length \ensuremathξa), we compute moments of the distributions, while for strong absorption (L\ensuremath≫\ensuremathξa), we can find the complete distributions. Our findings explain recent experiments on the transmittance of random waveguides by Stoytchev and Genack [Phys. Rev. Lett. 79, 309 (1997)].