Overdamped Brownian dynamics in piecewise-defined energy landscapes

• Main Authors: Gray, Thomas H., Yong, Ee Hou
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2021
• Subjects: Science::Physics; Brownian Motion; Glass Transition
• Online Access: https://hdl.handle.net/10356/146573
• Institution: Nanyang Technological University

We study the overdamped Brownian dynamics of particles moving in piecewise-defined potential energy landscapes U(x), where the height Q of each section is obtained from the exponential distribution p(Q)=aβexp(−aβQ), where β is the reciprocal thermal energy, and a>0. The averaged effective diffusion coefficient ⟨Deff⟩ is introduced to characterize the diffusive motion: ⟨x2⟩=2⟨Deff⟩t. A general expression for ⟨Deff⟩ in terms of U(x) and p(Q) is derived and then applied to three types of energy landscape: flat sections, smooth maxima, and sharp maxima. All three cases display a transition between subdiffusive and diffusive behavior at a=1, and a reduction to free diffusion as a→∞. The behavior of ⟨Deff⟩ around the transition is investigated and found to depend heavily upon the shape of the maxima: Energy landscapes made up of flat sections or smooth maxima display power-law behavior, while for landscapes with sharp maxima, strongly divergent behavior is observed. Two aspects of the subdiffusive regime are studied: the growth of the mean squared displacement with time and the distribution of mean first-passage times. For the former, agreement between Brownian dynamics simulations and a coarse-grained equivalent was observed, but the results deviated from the random barrier model's predictions. The discrepancy could be a finite-time effect. For the latter, agreement between the characteristic exponent calculated numerically and that predicted by the random barrier model is observed in the large-amplitude limit.