2013/04/30 by Santosh Kumar, André Nock, Hans-Jürgen Sommers +5 · 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:10.1103/physrevlett.111.030403
published as Physical Review Letters, Volume 111, Issue 3, Page 030403, Year 2013 · Published version
arxiv created 2013/07/18 · arxiv updated 2013/07/19
Scattering is an important phenomenon which is observed in systems ranging from the micro- to macroscale. In the context of nuclear reaction theory the Heidelberg approach was proposed and later demonstrated to be applicable to many chaotic scattering systems. To model the universal properties, stochasticity is introduced to the scattering matrix on the level of the Hamiltonian by using random matrices. A long-standing problem was the computation of the distribution of the off-diagonal scattering-matrix elements. We report here an exact solution to this problem and present analytical results for systems with preserved and with violated time-reversal invariance. Our derivation is based on a new variant of the supersymmetry method. We also validate our results with scattering data obtained from experiments with microwave billiards.