Tight-binding approach to overdamped Brownian motion on a bichromatic periodic potential
| Autor: | K. J. Challis, Phuong T.T. Nguyen, Michael W. Jack |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
0301 basic medicine
Length scale Physics Smoluchowski coagulation equation Basis (linear algebra) Models Theoretical 01 natural sciences Diffusion Maxima and minima Motion 03 medical and health sciences symbols.namesake 030104 developmental biology Classical mechanics Tight binding 0103 physical sciences Master equation symbols Orthonormal basis 010306 general physics Brownian motion |
| Zdroj: | Physical Review E. 93 |
| ISSN: | 2470-0053 2470-0045 |
| Popis: | We present a theoretical treatment of overdamped Brownian motion on a time-independent bichromatic periodic potential with spatially fast- and slow-changing components. In our approach, we generalize the Wannier basis commonly used in the analysis of periodic systems to define a basis of S states that are localized at local minima of the potential. We demonstrate that the S states are orthonormal and complete on the length scale of the periodicity of the fast-changing potential, and we use the S-state basis to transform the continuous Smoluchowski equation for the system to a discrete master equation describing hopping between local minima. We identify the parameter regime where the master equation description is valid and show that the interwell hopping rates are well approximated by Kramers' escape rate in the limit of deep potential minima. Finally, we use the master equation to explore the system dynamics and determine the drift and diffusion for the system. |
| Databáze: | OpenAIRE |
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