  We investigate the dynamics of an electron coupled to dispersionless optical
phonons in the Holstein model, at high temperatures. The dynamics is
conventionally believed to be diffusive, as the electron is repeatedly
scattered by optical phonons. In a semiclassical approximation, however, the
motion is not diffusive. In one dimension, the electron moves in a constant
direction and does not turn around. In two dimensions, the electron follows and
then continues to retrace a fractal trajectory. Aspects of these nonstandard
dynamics are retained in more accurate calculations, including a fully quantum
calculation of the electron and phonon dynamics.
