# Item

ITEM ACTIONSEXPORT

Released

Journal Article

#### Local equilibrium properties of ultraslow diffusion in the Sinai model

##### External Resource

No external resources are shared

##### Fulltext (restricted access)

There are currently no full texts shared for your IP range.

##### Fulltext (public)

2207.02936.pdf

(Preprint), 2MB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Padash, A., Aghion, E., Schulz, A., Barkai, E., Chechkin V, A., Metzler, R., et al. (2022).
Local equilibrium properties of ultraslow diffusion in the Sinai model.* New Journal of Physics,*
*24*(7): 073026. doi:10.1088/1367-2630/ac7df8.

Cite as: https://hdl.handle.net/21.11116/0000-000B-028A-7

##### Abstract

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.