  The combination of Rashba spin-orbit coupling and potential disorder induces
a random current operator for the edge states of a 2D topological insulator. We
prove that charge transport through such an edge is ballistic at any
temperature, with or without Luttinger liquid interactions. The solution
exploits a mapping to a spin 1/2 in a time-dependent field that preserves the
projection along one randomly undulating component (integrable dynamics). Our
result is exact and rules out random Rashba backscattering as a source of
temperature-dependent transport, absent integrability-breaking terms.
