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We study a chaotic quantum transport in the presence of a weak spin-orbitinteraction. Our theory covers the whole symmetry crossover regime betweentime-reversal invariant systems with and without a spin-orbit interaction. Thissituation is experimentally realizable when the spin-orbit interaction iscontrolled in a conductor by applying an electric field. We utilize asemiclassical approach which has recently been developed. In this approach, thenon-Abelian nature of the spin diffusion along a classical trajectory plays acrucial role. New analytical expressions with one crossover parameter aresemiclassically derived for the average conductance, conductance variance andshot noise. Moreover numerical results on a random matrix model describing thecrossover from the GOE (Gaussian Orthogonal Ensemble) to the GSE (GaussianSymplectic Ensemble) are compared with the semiclassical expressions.

Chaotic Transport in the Symmetry Crossover Regime with a Spin-orbit Interaction