Numerical study of the tight-binding approach to overdamped Brownian motion on a tilted periodic potential

K. J. Challis
Phys. Rev. E 94, 062123 – Published 19 December 2016

Abstract

We present a numerical study of the tight-binding approach to overdamped Brownian motion on a tilted periodic potential. In the tight-binding method the probability density is expanded on a basis of Wannier states to transform the Smoluchowski equation to a discrete master equation that can be interpreted in terms of thermal hopping between potential minima. We calculate the Wannier states and hopping rates for a variety of potentials, including tilted cosine and ratchet potentials. For deep potential minima the Wannier states are well localized and the hopping rates between nearest-neighbor states are qualitatively well described by Kramers' escape rate. The next-nearest-neighbor hopping rates are negative and must be negligible compared to the nearest-neighbor rates for the discrete master equation treatment to be valid. We find that the validity of the master equation extends beyond the quantitative applicability of Kramers' escape rate.

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  • Received 1 May 2016
  • Revised 29 November 2016

DOI:https://doi.org/10.1103/PhysRevE.94.062123

©2016 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

K. J. Challis

  • Scion, 49 Sala Street, Private Bag 3020, Rotorua 3046, New Zealand

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Issue

Vol. 94, Iss. 6 — December 2016

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