Markovian embedding of non-Markovian superdiffusion

Details Markovian embedding of non-Markovian superdiffusion Markovian embedding of non-Markovian superdiffusion

2009-10-02

arxiv.org/abs/0910.0393v2

Phys. Rev. E 81, 011136 (2010)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevE.81.011136

We consider different Markovian embedding schemes of non-Markovian stochastic processes that are described by generalized Langevin equations (GLE) and obey thermal detailed balance under equilibrium conditions. At thermal equilibrium superdiffusive behavior can emerge if the total integral of the memory kernel vanishes. Such a situation of vanishing static friction is caused by a super-Ohmic thermal bath. One of the simplest models of ballistic superdiffusion is determined by a bi-exponential memory kernel that was proposed by Bao [J.-D. Bao, J. Stat. Phys. 114, 503 (2004)]. We show that this non-Markovian model has infinitely many different 4-dimensional Markovian embeddings. Implementing numerically the simplest one, we demonstrate that (i) the presence of a periodic potential with arbitrarily low barriers changes the asymptotic large time behavior from free ballistic superdiffusion into normal diffusion; (ii) an additional biasing force renders the asymptotic dynamics superdiffusive again. The development of transients that display a qualitatively different behavior compared to the true large-time asymptotics presents a general feature of this non-Markovian dynamics. These transients though may be extremely long. As a consequence, they can be even mistaken as the true asymptotics. We find that such intermediate asymptotics exhibit a giant enhancement of superdiffusion in tilted washboard potentials and it is accompanied by a giant transient superballistic current growing proportional to $t^{\alpha_{{\rm eff}}}$ with an exponent $\alpha_{\rm eff}$ that can exceed the ballistic value of two.

Affiliated with

Also associated with

No associations

Rating

Markovian embedding of non-Markovian superdiffusion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Markovian embedding of non-Markovian superdiffusion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Markovian embedding of non-Markovian superdiffusion will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-26320