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The shot noise in the electrical current through a ballistic chaotic quantumdot with N-channel point contacts is suppressed for N --> infinity, because ofthe transition from stochastic scattering of quantum wave packets todeterministic dynamics of classical trajectories. The dynamics of the electronspin remains quantum mechanical in this transition, and can affect theelectrical current via spin-orbit interaction. We explain how the role of thechannel number N in determining the shot noise is taken over by the ratiol_{so}/lambda_F of spin precession length l_{so} and Fermi wave lengthlambda_F, and present computer simulations in a two-dimensional billiardgeometry (Lyapunov exponent alpha, mean dwell time tau_{dwell}, point contactwidth W) to demonstrate the scaling (lambda_F/l_{so})^{1/alpha tau_{dwell}} ofthe shot noise in the regime lambda_F << l_{so} << W.Comment: 4 pages, 3 figure

How spin-orbit interaction can cause electronic shot noise