  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.
