Spatial correlations in chaotic nanoscale systems with spin-orbit coupling

We investigate the statistical properties of wave functions in two-dimensional chaotic nanostructures with spin-orbit interactions.~ We are especially interested in the role that spin-orbit coupling plays on the spatial correlations of eigenfunctions.~ Numerical~results obtained from a scattering formalism [1] for a chaotic stadium billiard are compared with analytic results~from random matrix theory.~ We present results for the evolution of the wave function statistics as the spin-orbit interaction is varied.~ We also discuss consequences of these results on~spin-polarized tunneling experiments.\\[4pt] [1] M. G. E. da Luz, A. S. Lupu-Sax, and E. J. Heller. Phys. Rev. E 56, 2496 - 2507 (1997).