Related papers: Arnold diffusion in a pendulum lattice
Consider a symplectic map which possesses a normally hyperbolic invariant manifold of any even dimension with transverse homoclinic channels. We develop a topological shadowing argument to prove the existence of Arnold diffusion along the…
A lattice Boltzmann model with interacting particles was developed in order to simulate the magneto-rheological characteristics of magnetic fluids. In the frame of this model, $6\, +\,1$ species of particles are allowed to move across a…
A complete theory for the complex interaction between solar energetic particles and the turbulent interplanetary magnetic field remains elusive. In this work we aim to contribute towards such a theory by modelling the propagation of solar…
Examples of one-dimensional lattice systems are considered, in which patterns of different spatial scales arise alternately, so that the spatial phase over a full cycle undergo transformation according to expanding circle map that implies…
We study the large scale behavior of a collection of hard core run and tumble particles on a one dimensional lattice with periodic boundary conditions. Each particle has persistent motion in one direction decided by an associated spin…
We consider a tracer particle performing a random walk on a two-dimensional lattice in the presence of immobile hard obstacles. Starting from equilibrium, a constant force pulling on the particle is switched on, driving the system to a new…
In a diffusive conductor the eigenstates are spread over the entire sample. However, with certain probability, an anomalously localized state (ALS) can occur, i.e. the wave function assumes anomalously large values in some region of space.…
We consider a square expanding with constant speed seen from an observer moving away with constant acceleration and study the distribution of angles between rays from the observer towards the lattice points in the square. We prove the…
In this presentation we overview some recent results on biased tracer diffusion in lattice gases. We consider both models in which the gas particles density is explicitly conserved and situations in which the lattice gas particles undergo…
We present a numerical study of classical particles diffusing on a solid surface. The particles' motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic…
We study the electron dynamics in a 2D waveguide bounded by a periodically rippled surface in the presence of the time-periodic electric field. The main attention is paid to a possibility of a weak quantum diffusion along the coupling…
Over the last decade, an enormous interest and activity in complex networks have been witnessed within the physics community. On the other hand, diffusion and its theory, have equipped the toolbox of the physicist for decades. In this…
We experimentally study anomalous diffusion of ultra-cold atoms in a one dimensional polarization optical lattice. The atomic spatial distribution is recorded at different times and its dynamics and shape are analyzed. We find that the…
A $d$-dimensional branching diffusion, $Z$, is investigated, where the linear attraction or repulsion between particles is competing with an Ornstein-Uhlenbeck drift, with parameter $b$ (we take $b>0$ for inward O-U and $b<0$ for outward…
We consider the Anderson tight-binding model on $\mathbb{Z}^d$, $d\geq 2$, with Gaussian noise and at low disorder $\lambda>0$. We derive a diffusive scaling limit for the entries of the resolvent $R(z)$ at imaginary part…
A lattice Boltzmann model is introduced which simulates oil-water-surfactant mixtures. The model is based on a Ginzburg-Landau free energy with two scalar order parameters. Diffusive and hydrodynamic transport is included. Results are…
In a recent experiment [McGehee et al., Phys. Rev. Lett. 111, 145303 (2013)], the expansion of non-interacting ultracold fermions was studied in a random speckle potential, and the observed density profiles were interpreted based on 3D…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
Electrons at the Fermi energy may lose their ability to propagate to long distances in certain random media. We use Green functions and solve parquet equations for the non-local electron-hole vertex in high spatial dimensions to describe…
We analyze a trapping reaction with a single penetrable trap, in a one dimensional lattice, where both species (particles and trap) are mobile and have a drift velocity. We obtain the density as seen from a reference system attached to the…