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Dynamical zeta functions provide a powerful method to analyze low dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand even simple one dimensional maps can show an intricate structure of…
Predictions for deep Virtual Compton Scattering are obtained in a two-component dipole model of diffraction. The model automatically includes hard and soft components and implicitly allows for ``hadronic'' contributions via large dipoles.…
We derive and study a theoretical description for single file diffusion, i.e., diffusion in a one dimensional lattice of particles with hard core interaction. It is well known that for this system a tagged particle has anomalous diffusion…
We reconsider the problem of diffusion of particles at constant speed and present a generalization of the Telegrapher process to higher dimensional stochastic media ($d>1$), where the particle can move along $2^d$ directions. We derive the…
Using matter waves that are trapped in a deep optical lattice, dissipationless directed transport is demonstrated to occur if the single-band quantum dynamics is periodically tilted on one half of the lattice by a monochromatic field. Most…
We expand upon a new theoretical framework for Diffusion Limited Aggregation and associated Dielectric Breakdown Models in two dimensions [R. C. Ball and E. Somfai, Phys. Rev. Lett. 89, 135503 (2002)]. Key steps are understanding how these…
We present a Cartesian cut-cell finite-volume method for sharp-interface two-phase diffusion problems in static geometries. The formulation follows a two-fluid approach: independent diffusion equations are discretized in each phase on a…
We study the persistent random walk of photons on a one-dimensional lattice of random transmittances. Transmittances at different sites are assumed independent, distributed according to a given probability density $f(t)$. Depending on the…
We discuss diffusion of particles in a spatially inhomogeneous medium. From the microscopic viewpoint we consider independent particles randomly evolving on a lattice. We show that the reversibility condition has a discrete geometric…
Diffusion coefficients are obtained from linear response functions and from the quantal fluctuation dissipation theorem. They are compared with the results of both the theory of hydrodynamic fluctuations by Landau and Lifschitz as well as…
The particle diffusion in a fluid is a classical topic that dates back to more than one century ago. However, a full solution to this issue still lacks. In this work the velocity autocorrelation function and the diffusion constant are…
Self-interacting diffusions are processes living on a compact Riemannian manifold defined by a stochastic differential equation with a drift term depending on the past empirical measure of the process. The asymptotics of this measure is…
Consider the linear Boltzmann equation of radiative transfer in a half-space, with constant scattering coefficient $\sigma$. Assume that, on the boundary of the half-space, the radiation intensity satisfies the Lambert (i.e. diffuse)…
Infiltration of diffusing particles from one material to another where the diffusion mechanism is either normal or anomalous is a widely observed phenomena. When the diffusion is anomalous we find interesting behaviors: diffusion may lead…
The emergence of diffusion is one of the deepest physical phenomena observed in many-body interacting, chaotic systems. But establishing rigorously that correlation functions, say of the spin, expand diffusively, remains one of the most…
The problem of eliminating fast-relaxing variables to obtain an effective drift-diffusion process in position is solved in a uniform and straightforward way for models with velocity a function jointly of position and fast variables. A more…
We investigate wave propagation in rotationally symmetric tubes with a periodic spatial modulation of cross section. Using an asymptotic perturbation analysis, the governing quasi two-dimensional reaction-diffusion equation can be reduced…
An anomalous diffusion model for ion channel gating is put forward. This scheme is able to describe non-exponential, power-law like distributions of residence time intervals in several types of ion channels. Our method presents a…
We consider a drift-diffusion process with a time-independent and divergence-free random drift that is of white-noise character. We are interested in the critical case of two space dimensions, where one has to impose a small-scale cut-off…
The search for departures from standard hydrodynamics in many-body systems has yielded a number of promising leads, especially in low dimension. Here we study one of the simplest classical interacting lattice models, the nearest-neighbour…