Related papers: Super-Universal Behavior of Outliers Diffusing in …
We investigate the long time behavior of a passive particle evolving in a one-dimensional diffusive random environment, with diffusion constant $D$. We consider two cases: (a) The particle is pulled forward by a small external constant…
We study an ensemble of random walkers carrying internal noisy phase oscillators which are synchronized among the walkers by local interactions. Due to individual mobility, the interaction partners of every walker change randomly, hereby…
Superdiffusion arises when complicated, correlated and noisy motion at the microscopic scale conspires to yield peculiar dynamics at the macroscopic scale. It ubiquitously appears in a variety of scenarios, spanning a broad range of…
We show that particle transport in a uniform, quantum multi-baker map, is generically ballistic in the long time limit, for any fixed value of Planck's constant. However, for fixed times, the semi-classical limit leads to diffusion. Random…
This is a brief survey of recent experimental studies on out-of-equilibrium scaling laws, focusing on two prominent situations where non-trivial universality classes have been identified theoretically: absorbing-state phase transitions and…
We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous…
We have used kinetic Monte Carlo (kMC) simulations of a lattice gas to study front fluctuations in the spreading of a non-volatile liquid droplet onto a solid substrate. Our results are consistent with a diffusive growth law for the radius…
These notes are based on lectures delivered by the authors at a Langeoog seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a mixed audience of mathematicians and theoretical physicists. After a brief outline of the…
Processes involving bursts of activity separated by quiescent periods occur across diverse systems and scales. In human dynamics, these phenomena have been described by power-law inter-event time distributions, $P(t)\sim t^{-\alpha}$, with…
One of the main difficulties in proving convergence of discrete models of surface growth to the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher than one is that the correct way to take a scaling limit, so that the limit is…
Recent theoretical studies have gradually deepened our understanding of the one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) universality class even in the large deviation regime, but numerical methods for studying KPZ large deviations remain…
We study height fluctuations of interfaces in the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) class, growing at different speeds in the left half and the right half of space. Carrying out simulations of the discrete polynuclear growth…
We introduce a fractional Fokker-Planck equation with a temporal power-law dependence on the drift force fields. For this case, the moments of the tracer from the force-force correlation in terms of the time-dependent drift force fields are…
We explore the dynamics of two-dimensional massless Dirac-fermions within a quantum shutter approach, which involves the time-evolution of an initial cut-off plane wave. We show that the probability density is governed by an interplay…
We study the extremal dynamics emerging in an out-of-equilibrium one-dimensional Jepsen gas of $(N+1)$ hard-point particles. The particles undergo binary elastic collisions, but move ballistically in-between collisions. The gas is initally…
Stochastic motion of a point -- known as Brownian motion -- has many successful applications in science, thanks to its scale invariance and consequent universal features such as Gaussian fluctuations. In contrast, the stochastic motion of a…
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- hierarchical structure, spatial dynamics, and external driving -- are combined in a classical branching diffusion with…
Starting from a master equation in a quantum Hamiltonian form and a coupling to a heat bath we derive an evolution equation for a collective hopping process under the influence of a stochastic energy landscape. There results different…
We present a comprehensive numerical investigation of non-universal parameters and corrections related to interface fluctuations of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class, in d=1+1, for both flat and curved…
We consider the statistical properties of arrival times and balls on first-passage percolation (FPP) $2D$ square lattices with strong disorder in the link-times. A previous work showed a crossover in the weak disorder regime, between…