Tobias Guggenberger, Aleksei Chechkin, Ralf Metzler

• 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.