Absence of diffusion and fractal geometry in the Holstein model at high temperature

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.