Giant Acceleration of Free Diffusion by Use of Tilted Periodic Potentials

Abstract

The effective diffusion coefficient for the overdamped Brownian motion in a tilted periodic potential is calculated in closed analytical form. Universality classes and scaling properties for weak thermal noise are identified near the threshold tilt where deterministic running solutions set in. In this regime the diffusion may be greatly enhanced, as compared to free thermal diffusion with, for a realistic experimental setup, an enhancement of up to 14 orders of magnitude.

Enhanced Diffusion of Molecular Motors in the Presence of Adenosine Triphosphate and External Force

“…The mechanism of enhancement for high ATP concentrations is essentially the same as that in the case without ATP (i.e., the mechanism of diffusion enhancement in a tilted periodic potential 4,5 ). An alternative mechanism applies for low ATP concentrations, and the diffusion 19/22 enhancement is sensitive to how the transition rate depends on the displacement (rotation angle) of the motor.…”

“…The enhancement is possible when the system is driven away from the thermal equilibrium state, for example, by applying an external force [3][4][5][6] or by switching the potential (an on-off ratchet mechanism). 7,8 The diffusion coefficient can be increased considerably by tuning the strength of a constant external force, [3][4][5] the frequency of an unbiased ac force, 6 or the rate of potential switching.…”

“…7,8 The diffusion coefficient can be increased considerably by tuning the strength of a constant external force, [3][4][5] the frequency of an unbiased ac force, 6 or the rate of potential switching. 7,8 In the case of a particle in a one-dimensional periodic potential in the presence of a constant external force F (a particle in a tilted periodic potential), the diffusion coefficient as a * E-mail: sasaki@camp.apph.tohoku.ac.jp function of F exhibits a peak at a value close to the maximum slope F c of the potential; [3][4][5] note that in the absence of thermal noise, the particle remains stationary at a force-balanced location for F < F c while it continues to run in one direction ("running state") for F > F c . The reason for this diffusion enhancement is that the behavior of the particle, whether to remain in a potential well or to move to the adjacent well, is quite sensitive to thermal noise for F close to F c , which results in a large dispersion of the particle displacement and hence a large diffusion coefficient.…”

Entropy production, energy loss and currents in adiabatically rocked thermal ratchets

“…The coherent transport (optimal transport) refers to the case of large mean velocity at fairly small diffusion. It can be quantified [27,28,29,30] by a dimensionless Pećlet number. For a given magnitude of current transport may be coherent or incoherent.…”

A multiscale approach to Brownian motors

“…Furthermore, the number of theoretical studies related to the calculation of the effective diffusion tensor has also been scarce [12,20,31,32,35]. In these papers, relatively simple potentials and/or forcing terms are considered, such as tilting periodic potentials or simple periodic in time forcing.…”