Distribution of Scattering Matrix Elements in the case of Symplectic Symmetry

Abstract

Scattering theory is at the core of gaining information about most quantum systems. In general, analytic progress is difficult and the investigation of universal features using statistical methods is of interest. Commonly this is carried out within the Heidelberg approach which models the Hamiltonian of the target by a random matrix. Hitherto, such investigations were performed for systems that are effectively spinless or have total angular momentum conservation. In light of recent experimental progress it has become relevant to also investigate systems with half-integer spin. Using supersymmetry, we derive the distribution for the real and imaginary parts of the scattering matrix elements and the corresponding cross sections in the case of symplectic symmetry. These results complete the derivations for Dysons threefold way.