Related papers: Quenched localisation in the Bouchaud trap model w…
We consider the quenched localisation of the Bouchaud trap model on the positive integers in the case that the trap distribution has a slowly varying tail at infinity. Our main result is that for each $N \in \{2, 3, \ldots\}$ there exists a…
We consider the Bouchaud trap model on the integers in the case that the trap distribution has a slowly varying tail at infinity. We prove that the model eventually localises on exactly two sites with overwhelming probability. This is a…
It is well-known that both branching random walk models and trap models can exhibit intermittency and localisation phenomena; the prototypical examples being the parabolic Anderson and Bouchaud trap models respectively. Our aim is to…
We investigate the biased quenched trap model on top of a two-dimensional lattice in the case of diverging expected dwell times. By utilizing the double-subordination approach and calculating the return probability in $2$d, we explicitly…
In this work the diffusion in the quenched trap model with diverging mean waiting times is examined. The approach of randomly stopped time is extensively applied in order to obtain asymptotically exact representation of the disorder…
The Bouchaud-Anderson model (BAM) is a generalisation of the parabolic Anderson model (PAM) in which the driving simple random walk is replaced by a random walk in an inhomogeneous trapping landscape; the BAM reduces to the PAM in the case…
A trapping mechanism is observed and proposed as the origin of the anomalous behavior recently discovered in transport properties of overdamped ratchets subject to external oscillatory drive in the presence of quenched noise. In particular,…
Attributing a positive value \tau_x to each x in Z^d, we investigate a nearest-neighbour random walk which is reversible for the measure with weights (\tau_x), often known as "Bouchaud's trap model". We assume that these weights are…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
We study the equilibration behavior following local quenches, using frustrated quantum spin chains as an example of interacting closed quantum systems. Specifically, we examine the statistics of the time series of the Loschmidt echo, the…
Time-averaged trapping potentials have played an important role in the development of the field of ultracold atoms. Despite their widespread application, there is not yet a complete understanding of when a system can be considered…
Motivated by theoretical analyses of spatially localized structures with arbitrarily long periodic plateaus, we provide a framework of assumptions that simplifies their analysis and leads to a topological criterion for when localized…
This work focuses on quantitative representation of transport in systems with quenched disorder. Explicit mapping of the quenched trap model to continuous time random walk is presented. Linear temporal transformation: $t\to…
We study the equilibrium properties of an Ising model on a disordered random network where the disorder can be quenched or annealed. The network consists of four-fold coordinated sites connected via variable length one-dimensional chains.…
This paper is a first step in the study of the recurrence behavior in random dynamical systems and randomly perturbed dynamical systems. In particular we define a concept of quenched and annealed return times for systems generated by the…
We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and…
Closed quantum systems with quenched randomness exhibit many-body localized regimes wherein they do not equilibrate even though prepared with macroscopic amounts of energy above their ground states. We show that such localized systems can…
Stochastic processes with random reinforced relocations have been introduced in the physics literature to model animal foraging behaviour. Such a process evolves as a Markov process, except at random relocation times, when it chooses a time…
We study quenched mixing rates for two classes of random interval maps characterized by the presence of two indifferent fixed points and singular points. Using a random tower construction we prove the existence of an equivariant absolutely…
We study rates of mixing for small random perturbations of one dimensional Lorenz maps. Using a random tower construction, we prove that, for Holder observables, the random system admits exponential rates of quenched correlation decay.