Origin of dispersionless transport in spite of thermal noise

The ``dispersionless transport'' of a weakly damped Brownian particle in a tilted periodic potential is defined by (i) a plateau of the particle's coordinate dispersion extending over a very broad time interval and (ii) by the impossibility to measure the diffusion coefficient within this plateau region. While the first part of this definition has been explained in the literature, the second part has been thought to follow from (i). Here, the impossibility to measure the diffusion coefficient is shown to be actually due to the wild fluctuations of the dispersion itself in the plateau region. An expression for the timescale over which a reliable determination of the diffusion coefficient is possible is derived. A procedure that allows accurate determination of the diffusion coefficient by observing the particle trajectory only within a small part of the plateau region is suggested and shown to be feasible by numerical simulations of a weakly damped Brownian particle in a tilted washboard potential.