Related papers: Quantitative homogenization of degenerate random e…
We consider the problem of decoherence and relaxation of open bosonic quantum systems from a perspective alternative to the standard master equation or quantum trajectories approaches. Our method is based on the dynamics of expectation…
With recently developed tools, we prove a homogenisation theorem for a random ODE with short and long-range dependent fractional noise. The effective dynamics are not necessarily diffusions, they are given by stochastic differential…
The stationary states of boundary driven zero-range processes in random media with quenched disorder are examined, and the motion of a tagged particle is analyzed. For symmetric transition rates, also known as the random barrier model, the…
We study the homogenization of a stationary conductivity problem in a random heterogeneous medium with highly oscillating conductivity coefficients and an ensemble of simply closed conductivity resistant membranes. This medium is randomly…
Homogeneous fragmentations describe the evolution of a unit mass that breaks down randomly into pieces as time passes. They can be thought of as continuous time analogs of a certain type of branching random walks, which suggests the use of…
With a choice of boundary conditions for solutions of the Schr\"odinger equation, state vectors and density operators even for closed systems evolve asymmetrically in time. For open systems, standard quantum mechanics consequently predicts…
The behavior of particles driven through a narrow constriction is investigated in experiment and simulation. The system of particles adapts to the confining potentials and the interaction energies by a self-consistent arrangement of the…
We study the adsorption and desorption kinetics of interacting particles moving on a one-dimensional lattice. Confinement is introduced by limiting the number of particles on a lattice site. Adsorption and desorption are found to proceed at…
We consider a diffusion on a bounded domain, assuming that the system is irreducible inside the domain and that the diffusion has varying degree of degeneracy on the domain's boundary. The long-term statistical properties of typical…
We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
The diffusion of molecules in complex intracellular environments can be strongly influenced by spatial heterogeneity and stochasticity. A key challenge when modelling such processes using stochastic random walk frameworks is that negative…
We adapt and study a variance reduction approach for the homogenization of elliptic equations in divergence form. The approach, borrowed from atomistic simulations and solid-state science [von Pezold et al, Physical Review B 2010; Wei et…
In this paper, we introduce a random environment for the exclusion process in $\mathbb{Z}^d$ obtained by assigning a maximal occupancy to each site. This maximal occupancy is allowed to randomly vary among sites, and partial exclusion…
This paper proposes a linear categorical random coefficient model, in which the random coefficients follow parametric categorical distributions. The distributional parameters are identified based on a linear recurrence structure of moments…
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and…
The effect of diffusional relaxation on the random sequential deposition process is studied in the limit of fast deposition. Expression for the coverage as a function of time are analytically derived for both the short-time and long-time…
We consider connectivity properties of certain i.i.d. random environments on $\Z^d$, where at each location some steps may not be available. Site percolation and oriented percolation can be viewed as special cases of the models we consider.…
We study the relaxation process of two driven colloidal suspensions in diffusive contact to a steady state, similar to thermalization. We start by studying a single suspension, subjecting it to random driving forces via holographic optical…
We investigate the nonlocal behavior of passive tracer dispersion with random stopping at various sites in fluids. This kind of dispersion processes is modeled by an integral partial differential equation, i.e., an advection-diffusion…