  As devices to control spin currents using the spin-orbit interaction are
proposed and implemented, it is important to understand the fluctuations that
spin-orbit coupling can impose on transmission through a quantum dot. Using
random matrix theory, we estimate the typical scale of transmitted charge and
spin currents when a spin current is injected into a chaotic quantum dot with
strong spin-orbit coupling. These results have implications for the functioning
of the spin transistor proposed by Schliemann, Egues, and Loss. We use a
density matrix formalism appropriate for treating arbitrary input currents and
indicate its connections to the widely used spin-conductance picture. We
further consider the case of currents entangled between two leads, finding
larger fluctuations.
