Autocorrelation functions and ergodicity in diffusion with stochastic resetting
- Diffusion with stochastic resetting is a paradigm of resetting processes. Standard renewal or master equation approach are typically used to study steady state and other transport properties such as average, mean squared displacement etc. What remains less explored is the two time point correlation functions whose evaluation is often daunting since it requires the implementation of the exact time dependent probability density functions of the resetting processes which are unknown for most of the problems. We adopt a different approach that allows us to write a stochastic solution for a single trajectory undergoing resetting. Moments and the autocorrelation functions between any two times along the trajectory can then be computed directly using the laws of total expectation. Estimation of autocorrelation functions turns out to be pivotal for investigating the ergodic properties of various observables for this canonical model. In particular, we investigate two observables (i) sample mean which is widely used in economics andDiffusion with stochastic resetting is a paradigm of resetting processes. Standard renewal or master equation approach are typically used to study steady state and other transport properties such as average, mean squared displacement etc. What remains less explored is the two time point correlation functions whose evaluation is often daunting since it requires the implementation of the exact time dependent probability density functions of the resetting processes which are unknown for most of the problems. We adopt a different approach that allows us to write a stochastic solution for a single trajectory undergoing resetting. Moments and the autocorrelation functions between any two times along the trajectory can then be computed directly using the laws of total expectation. Estimation of autocorrelation functions turns out to be pivotal for investigating the ergodic properties of various observables for this canonical model. In particular, we investigate two observables (i) sample mean which is widely used in economics and (ii) time-averaged-mean-squared-displacement (TAMSD) which is of acute interest in physics. We find that both diffusion and drift-diffusion processes with resetting are ergodic at the mean level unlike their reset-free counterparts. In contrast, resetting renders ergodicity breaking in the TAMSD while both the stochastic processes are ergodic when resetting is absent. We quantify these behaviors with detailed analytical study and corroborate with extensive numerical simulations. Our results can be verified in experimental set-ups that can track single particle trajectories and thus have strong implications in understanding the physics of resetting.…
Author details: | Viktor Stojkoski, Trifce SandevORCiDGND, Ljupco Kocarev, Arnab PalORCiD |
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DOI: | https://doi.org/10.1088/1751-8121/ac4ce9 |
ISSN: | 1751-8113 |
ISSN: | 1751-8121 |
Title of parent work (English): | Journal of physics : A, Mathematical and theoretical |
Publisher: | IOP Publ. Ltd. |
Place of publishing: | Bristol |
Publication type: | Article |
Language: | English |
Date of first publication: | 2022/02/21 |
Publication year: | 2022 |
Release date: | 2024/06/14 |
Tag: | autocorrelations; diffusion; ergodicity; stochastic resetting |
Volume: | 55 |
Issue: | 10 |
Article number: | 104003 |
Number of pages: | 22 |
Funding institution: | German Science Foundation (DFG) [ME 1535/12-1]; Alexander von Humboldt; Foundation; Raymond and Beverly Sackler Post-Doctoral Scholarship;; Ratner Center for Single Molecule Science at Tel-Aviv University |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |
Publishing method: | Open Access / Hybrid Open-Access |
License (German): | CC-BY - Namensnennung 4.0 International |