2013/07/31 by André Nock, Santosh Kumar, Hans-Jürgen Sommers +1 · 1 citation
Physics and Astronomy · Mathematics · #cond-mat.stat-mech #math-ph #math.MP #nlin.CD #quant-ph #msc:15B52 #msc:60E05 #msc:60E10 #msc:81U35 #msc:82B31
paper · pdf · doi:10.1016/j.aop.2013.11.006
published as Annals of Physics, Volume 342, Pages 103-132, Year 2014 · 29 pages, 5 figures, Published version
arxiv created 2014/01/20 · arxiv updated 2014/01/21
Scattering is a ubiquitous phenomenon which is observed in a variety of physical systems which span a wide range of length scales. The scattering matrix is the key quantity which provides a complete description of the scattering process. The universal features of scattering in chaotic systems is most generally modeled by the Heidelberg approach which introduces stochasticity to the scattering matrix at the level of the Hamiltonian describing the scattering center. The statistics of the scattering matrix is obtained by averaging over the ensemble of random Hamiltonians of appropriate symmetry. We derive exact results for the distributions of the real and imaginary parts of the off-diagonal scattering matrix elements applicable to orthogonally-invariant and unitarily-invariant Hamiltonians, thereby solving a long standing problem.