First-passage statistics for aging diffusion in systems with annealed and quenched disorder.
Aging, the dependence of the dynamics of a physical process on the time ta since its original preparation, is observed in systems ranging from the motion of charge carriers in amorphous semiconductors over the blinking dynamics of quantum dots to the tracer dispersion in living biological cells. Here we study the effects of aging on one of the most fundamental properties of a stochastic process, the first-passage dynamics. We find that for an aging continuous time random walk process, the scaling exponent of the density of first-passage times changes twice as the aging progresses and reveals an intermediate scaling regime. The first-passage dynamics depends on ta differently for intermediate and strong aging. Similar crossovers are obtained for the first-passage dynamics for a confined and driven particle. Comparison to the motion of an aged particle in the quenched trap model with a bias shows excellent agreement with our analytical findings. Our results demonstrate how first-passage measurements can be used to unravel the age ta of a physical system.
Institute of Physics & Astronomy, University of Potsdam, 14776 Potsdam-Golm, Germany.
Henning
H
Krüsemann
Institute of Physics & Astronomy, University of Potsdam, 14776 Potsdam-Golm, Germany and National Institute of Chemistry, 1000 Ljubljana, Slovenia.
Aljaž
A
Godec
Institute of Physics & Astronomy, University of Potsdam, 14776 Potsdam-Golm, Germany and Department of Physics, Tampere University of Technology, FI-33101 Tampere, Finland.
Ralf
R
Metzler