Related papers: Scale invariance and dynamic phase transitions in …
The dynamics of a coupled two-component nonequilibrium system is examined by means of continuum field theory representing the corresponding master equation. Particles of species A may perform hopping processes only when particles of…
Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n=3,4 parents, whereas explicit diffusion of single particles (A) is present are investigated in low dimensions by…
We study diffusion-controlled single-species annihilation with a finite number of particles. In this reaction-diffusion process, each particle undergoes ordinary diffusion, and when two particles meet, they annihilate. We focus on spatial…
The theory of continuous phase transitions predicts the universal collective properties of a physical system near a critical point, which for instance manifest in characteristic power-law behaviours of physical observables. The…
Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population…
One of the most impressive features of continuous phase transitions is the concept of universality, that allows to group the great variety of different critical phenomena into a small number of universality classes. All systems belonging to…
Extensive simulations are performed of the diffusion-limited reaction A$+$B$\to 0$ in one dimension, with initially separated reagents. The reaction rate profile, and the probability distributions of the separation and midpoint of the…
The steady-state phase diagram of the one-dimensional reaction-diffusion model 2A -> 3A, 2A -> 0 is studied through the non-hermitian density matrix renormalization group. In the absence of single-particle diffusion the model reduces to the…
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…
Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…
We study the static and dynamic behavior of the one dimensional pair contact process with diffusion. Several critical exponents are found to vary with the diffusion rate, while the order-parameter moment ratio m=\bar{rho^2} /\bar{rho}^2…
We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical…
Recently Carlon et. al. investigated the critical behavior of the pair contact process with diffusion [cond-mat/9912347]. Using density matrix renormalization group methods, they estimate the critical exponents, raising the possibility that…
We investigate the critical behavior of a reaction-diffusion system exhibiting a continuous absorbing-state phase transition. The reaction-diffusion system strictly conserves the total density of particles, represented as a non-diffusive…
Models of reaction diffusion processes usually employ discrete lattice models with particles interacting at the same site, resulting in localized reactions in the continuum limit. Here, various non-local interactions are considered, and two…
The coupling of branching-annihilating random walks to a static field with a local conservation law is shown to change the scaling properties of their phase transitions to absorbing states. In particular, we find that DP-class transitions…
We investigate the quantum reaction-diffusion dynamics of fermionic particles which coherently hop in a one-dimensional lattice and undergo annihilation reactions. The latter are modelled as dissipative processes which involve losses of…
We study the absorbing phase transitions in coupled directed percolation (DP) processes with $N$-species particles in one dimension. The interspecies coupling is linear, bidirectional, and excitatory. We find that the presence of a…
We develop a microscopic theory for reaction-difusion (R-D) processes based on a generalization of Einstein's master equation with a reactive term and we show how the mean field formulation leads to a generalized R-D equation with…
We consider the diffusion-controlled annihilation dynamics $A+B\to 0$ with equal species diffusivities in the system where an island of particles $A$ is surrounded by the uniform sea of particles $B$. We show that once the initial number of…