TY  - JOUR
A1  - Guggenberger, Tobias
A1  - Chechkin, Aleksei
A1  - Metzler, Ralf
T1  - Absence of stationary states and non-Boltzmann distributions of fractional Brownian motion in shallow external potentials
T2  - New journal of physics : the open-access journal for physics
N2  - We study the diffusive motion of a particle in a subharmonic potential of the form U(x) = |x|( c ) (0 < c < 2) driven by long-range correlated, stationary fractional Gaussian noise xi ( alpha )(t) with 0 < alpha <= 2. In the absence of the potential the particle exhibits free fractional Brownian motion with anomalous diffusion exponent alpha. While for an harmonic external potential the dynamics converges to a Gaussian stationary state, from extensive numerical analysis we here demonstrate that stationary states for shallower than harmonic potentials exist only as long as the relation c > 2(1 - 1/alpha) holds. We analyse the motion in terms of the mean squared displacement and (when it exists) the stationary probability density function. Moreover we discuss analogies of non-stationarity of Levy flights in shallow external potentials.
KW  - diffusion
KW  - Boltzmann distribution
KW  - fractional Brownian motion
Y1  - 2022
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/62098
SN  - 1367-2630
VL  - 24
IS  - 7
PB  - Dt. Physikalische Ges.
CY  - [Bad Honnef]
ER  -