  The Fractional Langevin Equation (FLE) describes a non-Markovian Generalized
Brownian Motion with long time persistence (superdiffusion), or
anti-persistence (subdiffusion) of both velocity-velocity correlations, and
position increments. It presents a case of the Generalized Langevin Equation
(GLE) with a singular power law memory kernel. We propose and numerically
realize a numerically efficient and reliable Markovian embedding of this
superdiffusive GLE, which accurately approximates the FLE over many, about r=N
lg b-2, time decades, where N denotes the number of exponentials used to
approximate the power law kernel, and b>1 is a scaling parameter for the
hierarchy of relaxation constants leading to this power law. Besides its
relation to the FLE, our approach presents an independent and very flexible
route to model anomalous diffusion. Studying such a superdiffusion in tilted
washboard potentials, we demonstrate the phenomenon of transient hyperdiffusion
which emerges due to transient kinetic heating effects.
