Monday, April 22, 2013

1304.5284 (Santosh Kumar et al.)

Distribution of Scattering Matrix Elements in Quantum Chaotic Scattering    [PDF]

Santosh Kumar, André Nock, Hans-Jürgen Sommers, Thomas Guhr, Barbara Dietz, Maksim Miski-Oglu, Achim Richter, Florian Schäfer
Scattering is an important phenomenon which is observed in systems ranging from the micro to macro scale. 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.
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