  We present a field theoretic treatment of an adiabatic quantum motor. We
explicitly discuss a motor termed Thouless motor which is based on a Thouless
pump operating in reverse. When a sliding periodic potential is considered as
the motor degree of freedom, a bias voltage applied to the electron channel
sets the motor in motion. We investigate a Thouless motor whose electron
channel is modeled as a Luttinger liquid. Interactions increase the gap opened
by the periodic potential. For an infinite Luttinger liquid the coupling
induced friction is enhanced by electron-electron interactions. When the LL is
ultimately coupled to Fermi liquid reservoirs, the dissipation reduces to its
value for a noninteracting electron system for a constant motor velocity. Our
results can also be applied to a motor based on a nanomagnet coupled to a
quantum spin Hall edge.
