Breaking the Spin Degeneracy for Distributions of Off-Diagonal Scattering Matrix Elements in the Case of Symplectic Symmetry

Abstract: Recently derived exact expressions for the distributions of scattering matrix elements show that all combinations of ingoing and outgoing spin orientations are equally distributed. We propose a model suitable for experimental realization that breaks this degeneracy by introducing a spin preference in the channels. With the help of supersymmetry we derive a corresponding nonlinear sigma model. We exactly calculate the distributions of real and imaginary part in first order of the parameter measuring the preference. Quite remarkably, while breaking the spin degeneracy leads to different distributions for the favored and unfavored spin orientation, the real and imaginary parts of these altered distributions are the same as in the case of unbroken spin degeneracy.