  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.
