First exit times and residence times for discrete random walks on finite lattices

In this paper, we derive explicit formulas for the surface averaged first exit time of a discrete random walk on a finite lattice. We consider a wide class of random walks and lattices, including random walks in a non-trivial potential landscape. We also compute quantities of interest for modelling surface reactions and other dynamic processes, such as the residence time in a subvolume, the joint residence time of several particles and the number of hits on a reflecting surface.Comment: 19 pages, 2 figure

A reduced coupled-mode description for the electron-ion energy relaxation in dense matter

We present a simplified model for the electron-ion energy relaxation in dense two-temperature systems that includes the effects of coupled collective modes. It also extends the standard Spitzer result to both degenerate and strongly coupled systems. Starting from the general coupled-mode description, we are able to solve analytically for the temperature relaxation time in warm dense matter and strongly coupled plasmas. This was achieved by decoupling the electron-ion dynamics and by representing the ion response in terms of the mode frequencies. The presented reduced model allows for a fast description of temperature equilibration within hydrodynamic simulations and an easy comparison for experimental investigations. For warm dense matter, both fluid and solid, the model gives a slower electron-ion equilibration than predicted by the classical Spitzer result

Windings of the 2D free Rouse chain

We study long time dynamical properties of a chain of harmonically bound Brownian particles. This chain is allowed to wander everywhere in the plane. We show that the scaling variables for the occupation times T_j, areas A_j and winding angles \theta_j (j=1,...,n labels the particles) take the same general form as in the usual Brownian motion. We also compute the asymptotic joint laws P({T_j}), P({A_j}), P({\theta_j}) and discuss the correlations occuring in those distributions.Comment: Latex, 17 pages, submitted to J. Phys.

Heating mechanisms in radio frequency driven ultracold plasmas

Several mechanisms by which an external electromagnetic field influences the temperature of a plasma are studied analytically and specialized to the system of an ultracold plasma (UCP) driven by a uniform radio frequency (RF) field. Heating through collisional absorption is reviewed and applied to UCPs. Furthermore, it is shown that the RF field modifies the three body recombination process by ionizing electrons from intermediate high-lying Rydberg states and upshifting the continuum threshold, resulting in a suppression of three body recombination. Heating through collisionless absorption associated with the finite plasma size is calculated in detail, revealing a temperature threshold below which collisionless absorption is ineffective.Comment: 14 pages, 7 figure

Birkhoff type decompositions and the Baker-Campbell-Hausdorff recursion

We describe a unification of several apparently unrelated factorizations arisen from quantum field theory, vertex operator algebras, combinatorics and numerical methods in differential equations. The unification is given by a Birkhoff type decomposition that was obtained from the Baker-Campbell-Hausdorff formula in our study of the Hopf algebra approach of Connes and Kreimer to renormalization in perturbative quantum field theory. There we showed that the Birkhoff decomposition of Connes and Kreimer can be obtained from a certain Baker-Campbell-Hausdorff recursion formula in the presence of a Rota-Baxter operator. We will explain how the same decomposition generalizes the factorization of formal exponentials and uniformization for Lie algebras that arose in vertex operator algebra and conformal field theory, and the even-odd decomposition of combinatorial Hopf algebra characters as well as to the Lie algebra polar decomposition as used in the context of the approximation of matrix exponentials in ordinary differential equations.Comment: accepted for publication in Comm. in Math. Phy

Jamming transition in a homogeneous one-dimensional system: the Bus Route Model

We present a driven diffusive model which we call the Bus Route Model. The model is defined on a one-dimensional lattice, with each lattice site having two binary variables, one of which is conserved (``buses'') and one of which is non-conserved (``passengers''). The buses are driven in a preferred direction and are slowed down by the presence of passengers who arrive with rate lambda. We study the model by simulation, heuristic argument and a mean-field theory. All these approaches provide strong evidence of a transition between an inhomogeneous ``jammed'' phase (where the buses bunch together) and a homogeneous phase as the bus density is increased. However, we argue that a strict phase transition is present only in the limit lambda -> 0. For small lambda, we argue that the transition is replaced by an abrupt crossover which is exponentially sharp in 1/lambda. We also study the coarsening of gaps between buses in the jammed regime. An alternative interpretation of the model is given in which the spaces between ``buses'' and the buses themselves are interchanged. This describes a system of particles whose mobility decreases the longer they have been stationary and could provide a model for, say, the flow of a gelling or sticky material along a pipe.Comment: 17 pages Revtex, 20 figures, submitted to Phys. Rev.

From urn models to zero-range processes: statics and dynamics

The aim of these lecture notes is a description of the statics and dynamics of zero-range processes and related models. After revisiting some conceptual aspects of the subject, emphasis is then put on the study of the class of zero-range processes for which a condensation transition arises.Comment: Lecture notes for the Luxembourg Summer School 200