Interacting Brownian motion with resetting

Falcao, Ricardo; Evans, Martin R.

doi:10.1088/1742-5468/aa569c

Cited by 56 publications

(55 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Consequently, one can write a renewal equation for P r (J r , t), the probability that, at time t, the total current will have a value J r , P r (J r , t) = e −rt P 0 (J r , t) + r t 0 ds e −rs P 0 (J r , s). (44) Here P 0 (J r , s) denotes the probability that, starting from C 0 , in absence of resetting, J r number of particles cross the central bond until time s. We will use the above equation to explore P r (J r , t), but, first it is useful to investigate the mean and the variance of the total current.…”

Section: B Total Currentmentioning

confidence: 99%

“…Probability distribution of J r : Finally, we explore the behaviour of the probability distribution of the total current P r (J r , t) using the renewal equation (44). In the absence of resetting, the fluctuations of the total (diffusive) current are characterized by a Gaussian distribution in the long-time limit (see Appendix B 1 for more details).…”

Section: B Total Currentmentioning

confidence: 99%

See 1 more Smart Citation

Symmetric exclusion process under stochastic resetting

2019

View full text Add to dashboard Cite

We study the behaviour of a Symmetric Exclusion Process (SEP) in presence of stochastic resetting where the configuration of the system is reset to a step-like profile with a fixed rate r. We show that the presence of resetting affects both the stationary and dynamical properties of SEP strongly. We compute the exact time-dependent density profile and show that the stationary state is characterized by a non-trivial inhomogeneous profile in contrast to the flat one for r = 0. We also show that for r > 0 the average diffusive current grows linearly with time t, in stark contrast to the √ t growth for r = 0. In addition to the underlying diffusive current, we also identify the resetting current in the system which emerges due to the sudden relocation of the particles to the step-like configuration. We compute the probability distributions of the diffusive current and the total current (comprising of the diffusive and the resetting current) using the renewal approach. We demonstrate that while the typical fluctuations of the diffusive current around the mean are typically Gaussian, the distribution of the total current shows a strong non-Gaussian behaviour. arXiv:1906.11801v1 [cond-mat.stat-mech]

show abstract

Section: B Total Currentmentioning

confidence: 99%

Section: B Total Currentmentioning

confidence: 99%

Symmetric exclusion process under stochastic resetting

2019

View full text Add to dashboard Cite

show abstract

“…We can finally substitute formula (28) in Eq. (26) in order to get the explicit expression ofp ± (ω, s; x 0 ),…”

Section: Alternate Process With Resetsmentioning

confidence: 99%

“…More recently, in 2011, Evans and Majumdar [16,17] studied a diffusing model with a resetting term in a Fokker-Planck equation, derived from microscopical considerations. Afterwards, several analysis and generalizations of this formulation have been performed, including: The incorporation of an absorbing state [18]; the generalizations to d-spatial dimensions [19]; the presence of a general potential [20]; the inclusion of time dependency in the resetting rate [21] or a general distribution for the reset time [22]; a study of large deviations in Markovian processes [23]; a comparison with deterministic resetting [24]; the relocation to a previously position [25]; analyses on general properties of the first-passage time [26,27]; or the possibility that internal properties drive the reset mechanism of the system [28].…”

Section: Introductionmentioning

confidence: 99%

Continuous-time random walks with reset events

2017

View full text Add to dashboard Cite

In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant drift: the process moves in a fixed direction between the reset events, either by the effect of the random jumps, or by the action of a deterministic bias. However, the orientation of its motion is randomly determined after each restart. As a result of these alternating dynamics, interesting properties do emerge. General formulas for the propagator as well as for two extreme statistics, the survival probability and the mean first-passage time, are also derived. The rigor of these analytical results is verified by numerical estimations, for particular but illuminating examples.

show abstract

“…This model has been the focus of many studies [54][55][56]. The propose of the random walk process with resetting can be resumed by expression…”

Section: Random Walk Process With Stochastic Resetting and Memorymentioning

confidence: 99%

Non-Gaussian Distributions to Random Walk in the Context of Memory Kernels

Santos

2018

Fractal Fract

View full text Add to dashboard Cite

Abstract:The investigation of diffusive process in nature presents a complexity associated with memory effects. Thereby, it is necessary new mathematical models to involve memory concept in diffusion. In the following, I approach the continuous time random walks in the context of generalised diffusion equations. To do this, I investigate the diffusion equation with exponential and Mittag-Leffler memory-kernels in the context of Caputo-Fabrizio and Atangana-Baleanu fractional operators on Caputo sense. Thus, exact expressions for the probability distributions are obtained, in that non-Gaussian distributions emerge. I connect the distribution obtained with a rich class of diffusive behaviour. Moreover, I propose a generalised model to describe the random walk process with resetting on memory kernel context.

show abstract

Interacting Brownian motion with resetting

Cited by 56 publications

References 35 publications

Symmetric exclusion process under stochastic resetting

Symmetric exclusion process under stochastic resetting

Continuous-time random walks with reset events

Non-Gaussian Distributions to Random Walk in the Context of Memory Kernels

Contact Info

Product

Resources

About