Giant enhancement of diffusion and particle selection in rocked periodic potentials

– We investigate the motion of an overdamped Brownian particle in a periodic potential with weak thermal noise and a time-periodic unbiased (i.e. 〈F (t)〉 = 0) external driving force F (t). By introducing appropriate “waiting-periods”, where F (t) vanishes, an arbitrarily strong enhancement of diffusion in a symmetric potential is possible. In asymmetric periodic potentials (ratchets) the net flux of particles can be directed in both directions, even in the absence of thermal noise. For finite temperatures we observe and explain additional, pure-noise–induced flux reversal phenomena. Directed transport induced by unbiased driving forces in periodic structures with broken spatial symmetry (ratchets) has been investigated in the context of photovoltaic and photorefractive effects already for several decades [1]. Independent of such precursors, considerable interest in this scheme resurfaced with both theoretical [2] and experimental [3] recent activities that relate to the operation of Brownian machinery and molecular motors. On the other hand, the exploration of diffusive transport in completely symmetric, driven systems is still at its beginning [4-7]. In this letter we cover both modes of transport within a common model that allows a quite detailed analytical treatment. In addition, it should be possible to realize this set-up experimentally. In a first part, we modify the setup from [5, 6] so as to achieve a controlled selective enhancement of diffusion that in principle can be made arbitrarily strong. In the second part of our paper we introduce a new variant of the so-called “rocking ratchet” [8,9] for which the flux of particles can be directed in both directions even in the absence of thermal fluctuations, and which exhibits additional pure-noise–induced flux reversals as well. Control of diffusion. – We consider an overdamped Brownian particle with coordinate x(t) whose dynamics is governed by the Langevin equation ηẋ(t) = −V (x(t)) + F (t) + √ 2kTη ξ(t) . (1)