Heterogeneous diffusion with stochastic resetting
- 28 January 2022
- journal article
- research article
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 55 (7), 074003
- https://doi.org/10.1088/1751-8121/ac491c
Abstract
We study a heterogeneous diffusion process (HDP) with position-dependent diffusion coefficient and Poissonian stochastic resetting. We find exact results for the mean squared displacement and the probability density function. The nonequilibrium steady state reached in the long time limit is studied. We also analyse the transition to the non-equilibrium steady state by finding the large deviation function. We found that similarly to the case of the normal diffusion process where the diffusion length grows like t 1/2 while the length scale ξ(t) of the inner core region of the nonequilibrium steady state grows linearly with time t, in the HDP with diffusion length increasing like t p/2 the length scale ξ(t) grows like t p . The obtained results are verified by numerical solutions of the corresponding Langevin equation.Keywords
Funding Information
- Polish National Agency for Academic Exchange
- German Science Foundation (ME 1535/12-1)
- Alexander von Humboldt Foundation
- Fundacja na rzecz Nauki Polskiej, FNR
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