TY  - JOUR
A1  - Godec, Aljaz
A1  - Chechkin, Aleksei V.
A1  - Barkai, Eli
A1  - Kantz, Holger
A1  - Metzler, Ralf
T1  - Localisation and universal fluctuations in ultraslow diffusion processes
JF  - Journal of physics : A, Mathematical and theoretical
N2  - We study ultraslow diffusion processes with logarithmic mean squared displacement (MSD) < x(2)(t)> similar or equal to log(gamma)t. Comparison of annealed (renewal) continuous time random walks (CTRWs) with logarithmic waiting time distribution psi(tau) similar or equal to 1/(tau log(1+gamma)tau) and Sinai diffusion in quenched random landscapes reveals striking similarities, despite the great differences in their physical nature. In particular, they exhibit a weakly non-ergodic disparity of the time-averaged and ensemble-averaged MSDs. Remarkably, for the CTRW we observe that the fluctuations of time averages become universal, with an exponential suppression of mobile trajectories. We discuss the fundamental connection between the Golosov localization effect and non-ergodicity in the sense of the disparity between ensemble-averaged MSD and time-averaged MSD.
KW  - Sinai diffusion
KW  - anomalous diffusion
KW  - quenched energy landscape
Y1  - 2014
U6  - https://doi.org/10.1088/1751-8113/47/49/492002
SN  - 1751-8113
SN  - 1751-8121
VL  - 47
IS  - 49
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Padash, Amin
A1  - Aghion, Erez
A1  - Schulz, Alexander
A1  - Barkai, Eli
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
A1  - Kantz, Holger
T1  - Local equilibrium properties of ultraslow diffusion in the Sinai model
JF  - New journal of physics
N2  - We perform numerical studies of a thermally driven, overdamped particle in a random quenched force field, known as the Sinai model. We compare the unbounded motion on an infinite 1-dimensional domain to the motion in bounded domains with reflecting boundaries and show that the unbounded motion is at every time close to the equilibrium state of a finite system of growing size. This is due to time scale separation: inside wells of the random potential, there is relatively fast equilibration, while the motion across major potential barriers is ultraslow. Quantities studied by us are the time dependent mean squared displacement, the time dependent mean energy of an ensemble of particles, and the time dependent entropy of the probability distribution. Using a very fast numerical algorithm, we can explore times up top 10(17) steps and thereby also study finite-time crossover phenomena.
KW  - Sinai diffusion
KW  - clustering
KW  - local equilibrium
Y1  - 2022
U6  - https://doi.org/10.1088/1367-2630/ac7df8
SN  - 1367-2630
VL  - 24
IS  - 7
PB  - IOP Publishing
CY  - Bristol
ER  -