Related papers: Field-theoretic technique for irreversible reactio…
We consider a diffusion-limited reaction in case the reacting entities are not available simultaneously. Due to the fact that the reaction takes place after a spatiotemporal accumulation of reactants, the underlying rate equation has to be…
The dynamics of the one-dimensional spin-1/2 quantum XXZ model with random fields is investigated by the recurrence relations method. When the fields satisfy the bimodal distribution, the system shows a crossover between a collective-mode…
Renormalization group calculations for fluctuation-dominated reaction-diffusion systems are generally in agreement with simulations and exact solutions. However, simulations of the single-species reactions 3A->(0,A,2A) at their upper…
We review the field theory approach to percolation processes. Specifically, we focus on the so-called simple and general epidemic processes that display continuous non-equilibrium active to absorbing state phase transitions whose asymptotic…
Sinai's model of diffusion in one-dimension with random local bias is studied by a real space renormalization group which yields exact results at long times. The effects of an additional small uniform bias force are also studied. We obtain…
The behavior of the single-species reaction process $A+A\to O$ is examined near an impenetrable boundary, representing the flask containing the reactants. Two types of dynamics are considered for the reactants: diffusive and ballistic…
The $A + B\to 0$ diffusion-limited reaction, with equal initial densities $a(0) = b(0) = n_0$, is studied by means of a field-theoretic renormalization group formulation of the problem. For dimension $d > 2$ an effective theory is derived,…
The phase transitions to absorbing states of the branching-annihilating reaction-diffusion processes mA --> (m+k)A, nA --> (n-l)A are studied systematically in one space dimension within a new family of models. Four universality classes of…
We consider the effect of a random longitudinal field on the Ising model in a transverse magnetic field. For spatial dimension $d > 2$, there is at low strength of randomness and transverse field, a phase with true long range order which is…
We study the dynamics of simple reactions where the chemical species are confined on a general, time-modulated surface, and subjected to externally-imposed stirring. The study of these inhomogeneous effects requires a model based on a…
We apply the spectral method, recently developed by the authors, to calculate the statistics of a reaction-limited multi-step birth-death process, or chemical reaction, that includes as elementary steps branching A->2A and annihilation…
We investigate the kinetics of systems in which particles of one species undergo binary fragmentation and pair annihilation. In the latter, nonlinear process, fragments react at collision to produce an inert species, causing loss of mass.…
Presentation of the probability as an intrinsic property of the nature leads researchers to switch from deterministic to stochastic description of the phenomena. The procedure of stochastization of one-step process was formulated. It allows…
Sinai's model of diffusion in one-dimension with random local bias is studied by a real space renormalization group which yields asymptotically exact long time results. The distribution of the position of a particle and the probability of…
Infrared asymptotic behaviour of a scalar field, passively advected by a random shear flow, is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity is Gaussian, white in…
Standard field theoretic renormalization group is applied to the model of landscape erosion introduced by R. Pastor-Satorras and D. H. Rothman [Phys. Rev. Lett. 80: 4349 (1998); J. Stat. Phys. 93: 477 (1998)] yielding unexpected results:…
We derive a self-duality relation for a one-dimensional model of branching and annihilating random walkers with an even number of offsprings. With the duality relation and by deriving exact results in some limiting cases involving fast…
We address via numerical simulation the two-dimensional bimolecular annihilation reaction $A + A \to \emptyset$ in the presence of quenched, random impurities. Renormalization group calculations have suggested that this reaction displays…
We study effects of random fluid motion on a system in a self-organized critical state. The latter is described by the continuous stochastic model, proposed by Hwa and Kardar [{\it Phys. Rev. Lett.} {\bf 62}: 1813 (1989)]. The advecting…
We investigate several models described by real scalar fields, searching for topological defects, and investigating their linear stability. We also find bosonic zero modes and examine the thermal corrections at the one-loop level. The…