Ergodic properties of Brownian motion under stochastic resetting

被引:7
作者
Barkai, E. [1 ]
Flaquer-Galmes, R. [2 ]
Mendez, V. [2 ]
机构
[1] Bar Ilan Univ, Inst Nanotechnol & Adv Mat, Dept Phys, IL-52900 Ramat Gan, Israel
[2] Univ Autonoma Barcelona, Dept Fis, Grup Fis Estadist, Fac Ciencies, Barcelona 08193, Spain
基金
以色列科学基金会;
关键词
TIME;
D O I
10.1103/PhysRevE.108.064102
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
We study the ergodic properties of one-dimensional Brownian motion with resetting. Using generic classes of statistics of times between resets, we find respectively for thin-or fat-tailed distributions the normalized or non-normalized invariant density of this process. The former case corresponds to known results in the resetting literature and the latter to infinite ergodic theory. Two types of ergodic transitions are found in this system. The first is when the mean waiting time between resets diverges, when standard ergodic theory switches to infinite ergodic theory. The second is when the mean of the square root of time between resets diverges and the properties of the invariant density are drastically modified. We then find a fractional integral equation describing the density of particles. This finite time tool is particularly useful close to the ergodic transition where convergence to asymptotic limits is logarithmically slow. Our study implies rich ergodic behaviors for this nonequilibrium process which should hold far beyond the case of Brownian motion analyzed here.
引用
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页数:20
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