Quantum Friction and Casimir force of Unruh-deWitt detectors and plates.

We revisit the atom-plate quantum friction and Casimir force with a full-relativistic formalism for atoms modelled as Unruh-deWitt detectors in exited, relaxed and coherent superpositions close to a plate. We show that, for relative velocities close to c, the quantum friction diverges while the Casimir force is almost independent of the velocity. We are able to include the effect of the finite size of the detector, then we also obtain quantum friction when the detector is isolated but follows a non-inertial trajectory and we obtain a more realistic result for short distance interactions.