Related papers: Field-theoretic technique for irreversible reactio…
The behavior of the self diffusion constant of Langevin particles interacting via a pairwise interaction is considered. The diffusion constant is calculated approximately within a perturbation theory in the potential strength about the bare…
I explain the methods that are used in field theory for problems involving typical momenta on two or more widely disparate scales. The principal topics are: (a) renormalization, which treats the problem of taking an ultra-violet cut-off to…
We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Non-perturbative…
Numerical and theoretical studies of a one-dimensional spin model with locally broken spin symmetry are presented. The multi-species annihilating random walk transition found at zero branching rate previously is investigated now concerning…
The problem of the effects of compressibility and large-scale anisotropy on anomalous scaling behavior is considered for two models describing passive advection of scalar density and tracer fields. The advecting velocity field is Gaussian,…
The one-dimensional reaction diffusion process AA->A and A0A->AAA is exactly solvable through the empty interval method if the diffusion rate equals the coagulation rate. Independently of the particle production rate, the model is always in…
We study three basic diffusion-controlled reaction processes -- annihilation, coalescence, and aggregation. We examine the evolution starting with the most natural inhomogeneous initial configuration where a half-line is uniformly filled by…
The exact determination of ground states of small systems is used in a scaling study of the random-field Ising model. While three variants of the model are found to be in the same universality class in 3 dimensions, the Gaussian and bimodal…
The Ma-Dasgupta real-space renormalization methods allow to study disordered systems which are governed by strong disorder fixed points. After a general introduction to the qualitative ideas and to the quantitative renormalization rules, we…
The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is…
The dynamics of ecological as well as chemical systems may depend on heterogeneous configurations. Heterogeneity in reaction-diffusion systems often increase modelling and simulating difficulties when non-linear effects are present. One…
We investigate the problem of ballistically controlled reactions where particles either annihilate upon collision with probability $p$, or undergo an elastic shock with probability $1-p$. Restricting to homogeneous systems, we provide in…
We study nonlinear response in quantum spin systems {near infinite-randomness critical points}. Nonlinear dynamical probes, such as two-dimensional (2D) coherent spectroscopy, can diagnose the nearly localized character of excitations in…
This article is concerned with the fluctuations and the concentration properties of a general class of discrete generation and mean field particle interpretations of nonlinear measure valued processes. We combine an original stochastic…
We analyze from the renormalization group perspective a universality class of reaction-diffusion systems with absorbing states. It describes models where the vacuum state is not accessible, as the set of reactions $2 A \to A$ together with…
Random fields are commonly used for modeling of spatially (or timely) dependent stochastic processes. In this study, we provide a characterization of the intrinsic complexity of a random field in terms of its second order statistics, e.g.,…
The activity of catalytic materials is reduced during operation by several mechanisms, one of them being poisoning of catalytic sites by chemisorbed impurities or products. Here we study the effects of poisoning in two reaction-diffusion…
We consider a system of particles undergoing the branching and annihilating reactions A -> (m+1)A and A + A -> 0, with m even. The particles move via long-range Levy flights, where the probability of moving a distance r decays as…
A dilute system of reacting particles transported by fluid flows is considered. The particles react as $A + A \to \varnothing$ with a given rate when they are within a finite radius of interaction. The system is described in terms of the…
We introduce coarse-grained hydrodynamic equations of motion for diffusion-annihilation system with a power-law long-range interaction. By taking into account fluctuations of the conserved order parameter - charge density - we derive an…