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arXiv · 1604.04530

Noise-induced transitions in rugged energy landscapes

A. B. Duncan·S. Kalliadasis·G. A. Pavliotis·M. Pradas
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Abstract

We consider the problem of an overdamped Brownian particle moving in multiscale potential with N + 1 characteristic length scales: the macroscale and N separated microscales. We show that the coarse-grained dynamics is given by an overdamped Langevin equation with respect to the free energy and with a space dependent diffusion tensor, the calculation of which requires the solution of N fully coupled Poisson equations. We study in detail the structure of the bifurcation diagram for one-dimensional problems and we show that the multiscale structure in the potential leads to hysteresis effects and to noise-induced transitions. Furthermore, we obtain an explicit formula for the effective diffusion coefficient for a self-similar separable potential and we investigate the limit of infinitely many small scales.

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A. B. Duncan, S. Kalliadasis, G. A. Pavliotis, M. Pradas. 2016-04-14. Noise-induced transitions in rugged energy landscapes. https://doi.org/10.1103/physreve.94.032107

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