TY - JOUR
T1 - Anomalous diffusion and relaxation close to thermal equilibrium
T2 - A fractional fokker-planck equation approach
AU - Metzler, Ralf
AU - Barkai, Eli
AU - Klafter, Joseph
PY - 1999
Y1 - 1999
N2 - We introduce a fractional Fokker-Planck equation describing the stochastic evolution of a particle under the combined influence of an external, nonlinear force and a thermal heat bath. For the force-free case, a subdiffusive behavior is recovered. The equation is shown to obey generalized Einstein relations, and its stationary solution is the Boltzmann distribution. The relaxation of single modes is shown to follow a Mittag-Leffler decay. We discuss the example of a particle in a harmonic potential.
AB - We introduce a fractional Fokker-Planck equation describing the stochastic evolution of a particle under the combined influence of an external, nonlinear force and a thermal heat bath. For the force-free case, a subdiffusive behavior is recovered. The equation is shown to obey generalized Einstein relations, and its stationary solution is the Boltzmann distribution. The relaxation of single modes is shown to follow a Mittag-Leffler decay. We discuss the example of a particle in a harmonic potential.
UR - http://www.scopus.com/inward/record.url?scp=18144408075&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.82.3563
DO - 10.1103/PhysRevLett.82.3563
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AN - SCOPUS:18144408075
SN - 0031-9007
VL - 82
SP - 3563
EP - 3567
JO - Physical Review Letters
JF - Physical Review Letters
IS - 18
ER -