Correlation between diffusion and coherence in Brownian motion on a   tilted periodic potential
  The paper studies the overdamped motion of Brownian particles in a tilted sawtooth potential. The dependencies of the diffusion coefficient and coherence level of Brownian transport on temperature, tilting force, and the shape of the potential are analyzed. It is demonstrated that at low temperatures the coherence level of Brownian transport stabilizes in the extensive domain of the tilting force where the value of the Peclet factor is Pe=2. This domain coincides with the one where the enhancement of the diffusion coefficient versus the tilting force is the most rapid. The necessary and sufficient conditions for the non-monotonic behaviour of the diffusion coefficient as a function of temperature are found. The effect of the acceleration of diffusion by bias and temperature is demonstrated to be very sensitive to the value of the asymmetry parameter of the potential. 
E.Heinsalu, R.Tammelo, T.Ord