English
Related papers

Related papers: Non-ergodicity, fluctuations, and criticality in h…

200 papers

Time averages extracted from single-particle trajectories in complex media often vary strongly from one trajectory to another, even for long measurement times. Such persistent trajectory-to trajectory scatter is commonly observed in…

Statistical Mechanics · Physics 2026-03-18 Dan Shafir , Stanislav Burov

The nature of diffusion is usually studied for particles or time-evolving systems. Similar in principle, such studies can be conducted by tracking how a given function of observable properties evolves over time-akin to the evolution of…

Statistical Mechanics · Physics 2026-03-10 M. Süzen

The L\'evy walk model is a stochastic framework of enhanced diffusion with many applications in physics and biology. Here we investigate the time averaged mean squared displacement $\bar{\delta^2}$ often used to analyze single particle…

Statistical Mechanics · Physics 2014-06-03 Daniela Froemberg , Eli Barkai

We present a modelling approach for diffusion in a complex medium characterized by a random length scale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single particle tracking experiments…

Statistical Mechanics · Physics 2016-12-14 Daniel Molina-García , Tuan Minh Pham , Paolo Paradisi , Carlo Manzo , Gianni Pagnini

Diffusion is a central phenomenon in almost all fields of natural science revealing microscopic processes from the observation of macroscopic dynamics. Here, we consider the paradigmatic system of a single atom diffusing in a periodic…

We study the motion of a particle sliding under the action of an external field on a stochastically fluctuating one-dimensional Edwards-Wilkinson surface. Numerical simulations using the single-step model shows that the mean-square…

Statistical Mechanics · Physics 2009-11-10 Manoj Gopalakrishnan

Resetting or restart, when applied to a stochastic process, usually brings its dynamics to a time-independent stationary state. In turn, the optimal resetting rate makes the mean time to reach a target to be the shortest one. These and…

Statistical Mechanics · Physics 2022-08-31 Przemyslaw Chelminiak

We study the ergodic properties of superdiffusive, spatiotemporally coupled Levy walk processes. For trajectories of finite duration, we reveal a distinct scatter of the scaling exponents of the time averaged mean squared displacement…

Statistical Mechanics · Physics 2015-06-11 Aljaz Godec , Ralf Metzler

We propose a model of sub-diffusion in which an external force is acting on a particle at all times not only at the moment of jump. The implication of this assumption is the dependence of the random trapping time on the force with the…

Statistical Mechanics · Physics 2015-04-16 Sergei Fedotov , Nickolay Korabel

A tracer particle is called anomalously diffusive if its mean squared displacement grows approximately as $\sigma^2 t^{\alpha}$ as a function of time $t$ for some constant $\sigma^2$, where the diffusion exponent satisfies $\alpha \neq 1$.…

Soft Condensed Matter · Physics 2018-10-17 Kui Zhang , Katelyn P. R. Crizer , Mark H. Schoenfisch , David B. Hill , Gustavo Didier

We present a systematic study of dynamical heterogeneity in a model for permanent gels, upon approaching the gelation threshold. We find that the fluctuations of the self intermediate scattering function are increasing functions of time,…

Soft Condensed Matter · Physics 2009-11-19 T. Abete , A. de Candia , E. Del Gado , A. Fierro , A. Coniglio

We consider the problem of diffusion with stochastic resetting in a population of random walks where the diffusion coefficient is not constant, but behaves as a power-law of the average resetting rate of the population. Resetting occurs…

Statistical Mechanics · Physics 2022-09-07 Eric Bertin

In this paper, we study solutions of the heterogeneous diffusion process with power-law nonlinearity governed by the stochastic differential equation $\mathrm{d}X_t= |X_t|^\alpha\,\mathrm{d}B_t + \alpha\lambda…

Probability · Mathematics 2025-12-02 Jorge E. Cardona , Ilya Pavlyukevich

In this paper, we study the basic problem of a charged particle in a stochastic magnetic field. We consider dichotomous fluctuations of the magnetic field {where the sojourn time in one of the two states are distributed according to a given…

Disordered Systems and Neural Networks · Physics 2021-06-28 Gerardo Aquino , Kristopher J. Chandia , Mauro Bologna

We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth…

Statistical Mechanics · Physics 2016-10-05 A. G. Cherstvy , R. Metzler

Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of…

Statistical Mechanics · Physics 2016-12-21 Takuma Akimoto , Eiji Yamamoto

We consider Langevin equation with dichotomously fluctuating diffusivity, where the diffusion coefficient changes dichotomously in time, in order to study fluctuations of time-averaged observables in temporary heterogeneous diffusion…

Statistical Mechanics · Physics 2016-06-15 Takuma Akimoto , Eiji Yamamoto

A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…

Statistical Mechanics · Physics 2018-11-26 V. Sposini , A. V. Chechkin , F. Seno , G. Pagnini , R. Metzler

We study the long time behavior (homogenization) of a diffusion in random medium with time and space dependent coefficients. The diffusion coefficient may degenerate. In Stochastic Process. Appl. (2007) (to appear), an invariance principle…

Probability · Mathematics 2008-08-26 Rémi Rhodes

We extend recent results on the exact hydrodynamics of a system of diffusive active particles displaying a motility-induced phase separation to account for typical fluctuations of the dynamical fields. By calculating correlation functions…

Statistical Mechanics · Physics 2021-08-26 Tal Agranov , Sunghan Ro , Yariv Kafri , Vivien Lecomte