TY  - JOUR
A1  - Guggenberger, Tobias
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Fractional Brownian motion in superharmonic potentials and non-Boltzmann stationary distributions
T2  - Journal of physics : A, Mathematical and theoretical
N2  - We study the stochastic motion of particles driven by long-range correlated fractional Gaussian noise (FGN) in a superharmonic external potential of the form U(x) proportional to x(2n) (n is an element of N). When the noise is considered to be external, the resulting overdamped motion is described by the non-Markovian Langevin equation for fractional Brownian motion. For this case we show the existence of long time, stationary probability density functions (PDFs) the shape of which strongly deviates from the naively expected Boltzmann PDF in the confining potential U(x). We analyse in detail the temporal approach to stationarity as well as the shape of the non-Boltzmann stationary PDF. A typical characteristic is that subdiffusive, antipersistent (with negative autocorrelation) motion tends to effect an accumulation of probability close to the origin as compared to the corresponding Boltzmann distribution while the opposite trend occurs for superdiffusive (persistent) motion. For this latter case this leads to distinct bimodal shapes of the PDF. This property is compared to a similar phenomenon observed for Markovian Levy flights in superharmonic potentials. We also demonstrate that the motion encoded in the fractional Langevin equation driven by FGN always relaxes to the Boltzmann distribution, as in this case the fluctuation-dissipation theorem is fulfilled.
KW  - anomalous diffusion
KW  - Boltzmann distribution
KW  - non-Gaussian distribution
Y1  - 2021
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/58684
SN  - 1751-8113
SN  - 1751-8121
VL  - 54
IS  - 29
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -