  Phonon scattering calculations predict the drag force acting on defects and
dislocations rises linearly with temperature, in direct contradiction with
molecular dynamics simulations that often finds the drag force to be
independent of temperature. Using the Mori-Zwanzig projection technique, with
no recourse to elasticity or scattering theories, we derive a general Langevin
equation for a crystal defect, with full treatment of discreteness and
non-linearity in the defect core. We obtain an analytical expression for the
drag force that is evaluated in molecular statics and molecular dynamics,
extracting the force on a defect directly from the inter-atomic forces. Our
results show that a temperature independent drag force arises because
vibrations in a discrete crystal are never independent of the defect motion, an
implicit assumption in any phonon-based approach. This effect remains even when
the Peierls barrier is effectively zero, invalidating qualitative explanations
involving the radiation of phonons. We apply our methods to an interstitial
defect in tungsten and solitons in the Frenkel-Kontorova model, finding very
good agreement with trajectory-based estimations of the thermal drag force.
