  We investigate anomalous diffusion processes governed by the fractional
Langevin equation and confined to a finite or semi-infinite interval by
reflecting potential barriers. As the random and damping forces in the
fractional Langevin equation fulfill the appropriate fluctuation-dissipation
relation, the probability density on a finite interval converges for long times
towards the expected uniform distribution prescribed by thermal equilibrium. In
contrast, on a semi-infinite interval with a reflecting wall at the origin, the
probability density shows pronounced deviations from the Gaussian behavior
observed for normal diffusion. If the correlations of the random force are
persistent (positive), particles accumulate at the reflecting wall while
anti-persistent (negative) correlations lead to a depletion of particles near
the wall. We compare and contrast these results with the strong accumulation
and depletion effects recently observed for non-thermal fractional Brownian
motion with reflecting walls, and we discuss broader implications.
