  In a two-dimensional quantum dot in a GaAs heterostructure, the spin-orbit
scattering rate is substantially reduced below the rate in a bulk
two-dimensional electron gas [B.I. Halperin et al, Phys. Rev. Lett. 86, 2106
(2001)]. Such a reduction can be undone if the spin-orbit coupling parameters
acquire a spatial dependence, which can be achieved, e.g., by a metal gate
covering only a part of the quantum dot. We calculate the effect of such
spatially non-uniform spin-orbit scattering on the weak localization correction
and the universal conductance fluctuations of a chaotic quantum dot coupled to
electron reservoirs by ballistic point contacts, in the presence of a magnetic
field parallel to the plane of the quantum dot.
