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We investigate the dynamics of an electron coupled to dispersionless opticalphonons in the Holstein model, at high temperatures. The dynamics isconventionally believed to be diffusive, as the electron is repeatedlyscattered by optical phonons. In a semiclassical approximation, however, themotion is not diffusive. In one dimension, the electron moves in a constantdirection and does not turn around. In two dimensions, the electron follows andthen continues to retrace a fractal trajectory. Aspects of these nonstandarddynamics are retained in more accurate calculations, including a fully quantumcalculation of the electron and phonon dynamics.

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