https://doi.org/10.1140/epje/s10189-022-00176-4
Regular Article - Soft Matter
Brownian particles driven by spatially periodic noise
1
Institut für Theoretische Physik II: Weiche Materie, Heinrich, Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany
2
University of Lille, UGSF CNRS UMR8576, 59000, Lille, France
Received:
19
November
2021
Accepted:
18
February
2022
Published online:
1
March
2022
We discuss the dynamics of a Brownian particle under the influence of a spatially periodic noise strength in one dimension using analytical theory and computer simulations. In the absence of a deterministic force, the Langevin equation can be integrated formally exactly. We determine the short- and long-time behaviour of the mean displacement (MD) and mean-squared displacement (MSD). In particular, we find a very slow dynamics for the mean displacement, scaling as 
with time t. Placed under an additional external periodic force near the critical tilt value we compute the stationary current obtained from the corresponding Fokker–Planck equation and identify an essential singularity if the minimum of the noise strength is zero. Finally, in order to further elucidate the effect of the random periodic driving on the diffusion process, we introduce a phase factor in the spatial noise with respect to the external periodic force and identify the value of the phase shift for which the random force exerts its strongest effect on the long-time drift velocity and diffusion coefficient
© The Author(s) 2022
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