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Noise-induced transitions in rugged energy landscapes

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posted on 2023-06-09, 06:43 authored by A B Duncan, S Kalliadasis, G A Pavliotis, M Pradas
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 equationwith 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.

History

Publication status

  • Published

File Version

  • Published version

Journal

Physical Review E

ISSN

2470-0045

Publisher

American Physical Society

Issue

3

Volume

94

Page range

032107

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2017-06-15

First Open Access (FOA) Date

2017-06-15

First Compliant Deposit (FCD) Date

2017-06-15

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