Related papers: Equilibrium Perturbations for Asymmetric Zero Rang…
A conserved generalized zero range process is considered in which two sites interact such that particles hop from the more populated site to the other with a probability $p$. The steady state particle distribution function $P(n)$ is…
The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…
We generalize leading-order asymptotics of a form of the heat content of a submanifold (van den Berg & Gilkey 2015) to the setting of time-dependent diffusion processes in the limit of vanishing diffusivity. Such diffusion processes arise…
Annihilation processes, where the reacting particles are influenced by some external advective field, are one of the simplest examples of nonlinear statistical systems. This type of processes can be observed in miscellaneous chemical,…
We consider some interacting particle processes with long-range dynamics: the zero-range and exclusion processes with long jumps. We prove that the hydrodynamic limit of these processes corresponds to a (possibly non-linear) fractional heat…
The asymmetric exclusion process is an idealised stochastic model of transport, whose exact solution has given important insight into a general theory of nonequilibrium statistical physics. In this work, we consider a totally asymmetric…
Zero-range processes with decreasing jump rates exhibit a condensation transition, where a positive fraction of all particles condenses on a single lattice site when the total density exceeds a critical value. We study the onset of…
The diffusivity $D(t)$ of finite-range asymmetric exclusion processes on $\mathbb Z$ with non-zero drift is expected to be of order $t^{1/3}$. Sepp\"{a}l\"ainen and Bal\'azs recently proved this conjecture for the nearest neighbor case. We…
We study a supersymmetric model in curved background spacetime. We calculate the effective action and the vacuum expectation value of the energy momentum tensor using a covariant regularization procedure. A soft supersymmetry breaking…
We consider the asymmetric exclusion process (ASEP) in one dimension on sites $i = 1,..., N$, in contact at sites $i=1$ and $i=N$ with infinite particle reservoirs at densities $\rho_a$ and $\rho_b$. As $\rho_a$ and $\rho_b$ are varied, the…
We consider a one-dimensional, weakly asymmetric, boundary driven exclusion process on the interval $[0,N]\cap Z$ in the super-diffusive time scale $N^2 \epsilon^{-1}_N$, where $1\ll \epsilon^{-1}_N \ll N^{1/4}$. We assume that the external…
Influence of strong uniaxial small-scale anisotropy on the stability of inertial-range scaling regimes in a model of a passive transverse vector field advected by an incompressible turbulent flow is investigated by means of the field…
We consider ${\rm U}(1)$-symmetric scalar quantum field theories at zero temperature. At nonzero charge densities, the ground state of these systems is usually assumed to be a superfluid phase, in which the global symmetry is spontaneously…
In this article, we consider the problem of homogenising the linear heat equation perturbed by a rapidly oscillating random potential. We consider the situation where the space-time scaling of the potential's oscillations is \textit{not}…
We consider the dynamics of diffusing particles in one space dimension with annihilation on collision and nucleation (creation of particles) with constant probability per unit time and length. The cases of nucleation of single particles and…
In charged fluids obeying particle-hole symmetry, such as the Dirac fluid in graphene, charge transport is diffusive despite the presence of ballistically propagating sound waves: sound waves "hydrodynamically decouple" from the slower…
A diffusion-limited annihilation process, A+B->0, with species initially separated in space is investigated. A heuristic argument suggests the form of the reaction rate in dimensions less or equal to the upper critical dimension $d_c=2$.…
We study the generalized $n$ component model of a driven diffusive system with annealed random drive in the large $n$ limit. This non-equilibrium model also describes conserved order parameter dynamics of an equilibrium model of…
Let $\bb T_L = \bb Z/L \bb Z$ be the one-dimensional torus with $L$ points. For $\alpha >0$, let $g: \bb N\to \bb R_+$ be given by $g(0)=0$, $g(1)=1$, $g(k) = [k/(k-1)]^\alpha$, $k\ge 2$. Consider the totally asymmetric zero range process…
We show random polymer is diffusive in dimensions 1 and 2 in probability in an intermediate scaling regime. The scale is $\beta= o(N^{-1/4})$ in d=1 and $\beta=o((\log N)^{-1/2})$ in $d=2$ as $N\rightarrow \infty$.