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Exact Results for Spectra of Overdamped Brownian Motion in Fixed and Randomly Switching Potentials

A. A. Dubkov·V. N. Ganin·B. Spagnolo
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Abstract

The exact formulae for spectra of equilibrium diffusion in a fixed bistable piecewise linear potential and in a randomly flipping monostable potential are derived. Our results are valid for arbitrary intensity of driving white Gaussian noise and arbitrary parameters of potential profiles. We find: (i) an exponentially rapid narrowing of the spectrum with increasing height of the potential barrier, for fixed bistable potential; (ii) a nonlinear phenomenon, which manifests in the narrowing of the spectrum with increasing mean rate of flippings, and (iii) a nonmonotonic behaviour of the spectrum at zero frequency, as a function of the mean rate of switchings, for randomly switching potential. The last feature is a new characterization of resonant activation phenomenon.

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A. A. Dubkov, V. N. Ganin, B. Spagnolo. 2004-03-27. Exact Results for Spectra of Overdamped Brownian Motion in Fixed and Randomly Switching Potentials. https://arxiv.org/abs/cond-mat/0403664

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