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We study quantum percolation which is described by a tight-binding Hamiltonian containing only off-diagonal hopping terms that are generally in quenched binary disorder (zero or one). In such a system, transmission of a quantum particle is…

The effects of quenched disorder on the overdamped motion of a driven particle on a periodic, asymmetric potential is studied. While for the unperturbed potential the transport is due to a regular drift, the quenched disorder induces a…

We study the transport properties of a system of active particles moving at constant speed in an heterogeneous two-dimensional space. The spatial heterogeneity is modeled by a random distribution of obstacles, which the active particles…

We determine the propagation properties of a quantum particle in a d-dimensional lattice with hopping disorder, delta-correlated in time. The system is delocalized: the averaged transition probability shows a diffusive behavior. Then,…

We study the dynamics of an ideal polymer chain in a crowded, viscoelastic medium and in the presence of active forces. The motion of the centre of mass and of individual monomers is calculated. On time scales that are comparable to the…

The more we learn about the cytoplasm of cells, the more we realise that the cytoplasm is not uniform but instead is highly inhomogeneous. In any inhomogeneous solution, there are concentration gradients, and particles move either up or…

We investigate the dynamics of a quantum particle in disordered tight-binding models in one and two dimensions which are exceptions to the common wisdom on Anderson localization, in the sense that the localization length diverges at some…

We introduce two discrete models of a collection of colliding particles with stored momentum and study the asymptotic growth of the mean-square displacement of an active particle. We prove that the models are superdiffusive in one dimension…

We use coarse grained molecular dynamics simulations to investigate diffusion properties of sheared lipid membranes with embedded transmembrane proteins. In membranes without proteins, we find normal in-plane diffusion of lipids in all flow…

Heterogeneous distribution of passive and active domains in the chromosome plays a crucial role for its dynamic organization within the cell nucleus. Motivated by that here we investigate the steady-state conformation and dynamics of a…

We study the disorder-induced deterministic dispersion of particles uniformly driven in an array of narrow tracks. For different toy models with quenched disorder we obtain exact analytical expressions for the steady-state mean velocity $v$…

A topic of intense current investigation pursues the question how the highly crowded environment of biological cells affects the dynamic properties of passively diffusing particles. Motivated by recent experiments we report results of…

In this work we study the transport properties of non-interacting overdamped particles, moving on tilted disordered potentials, subjected to Gaussian white noise. We give exact formulas for the drift and diffusion coefficients for the case…

We investigate dynamically and statistically diffusive motion in a Klein-Gordon particle chain in the presence of disorder. In particular, we examine a low energy (subdiffusive) and a higher energy (self-trapping) case and verify that…

Static or frozen disorder, characterised by spatial heterogeneities, influences diverse complex systems, encompassing many-body systems, equilibrium and nonequilibrium states of matter, intricate network topologies, biological systems, and…

We study an active random walker model in which a particle's motion is determined by a self-generated field. The field encodes information about the particle's path history. This leads to either self-attractive or self-repelling behavior.…

Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…

We study the effect of disorder on the particle density evolution in a classical Hamiltonian driven lattice setup. If the disorder is localized within a finite sub-domain of the lattice, the emergence of strong tails in the density…

The dynamics of dense particle packings near the jamming transition is characterized by correlated particle motion. The growth of dynamical heterogeneities, or strong spatial variations in the motion of the particles constituting the…

In this work we study the spreading dynamics of tiny liquid droplets on solid surfaces in the case where the ends of the molecules feel different interactions with respect to the surface. We consider a simple model of dimers and short…