Dephasing in Rashba spin precession along mutlichannel quantum wires and nanotubes

Coherent Rashba spin precession along interacting multi-mode quantum channels is investigated, revisiting the theory of coupled Tomonaga-Luttinger liquids. We identify susceptibilities as the key-parameters to govern exponents and Rashba precession lengths. In semiconducting quantum wires spins of different transport channels are found to {\em dephase} in their respective precession angles with respect to one another, as a result of the interaction. This could explain the experimental difficulty to realize the Datta Das transistor. In single walled carbon nanotubes, on the other hand, interactions are predicted to suppress dephasing between the two flavor modes at small doping.