Diffusion-annihilation dynamics in one spatial dimension

We discuss a reaction-diffusion model in one dimension subjected to an external driving force. Each lattice site may be occupied by at most one particle. The particles hop with asymmetric rates (the sum of which is one) to the right or left nearest neighbour site if it is vacant, and annihilate with rate one if it is occupied. We compute the long time behaviour of the space dependent average density in states where the initial density profiles are step functions. We also compute the exact time dependence of the particle density for uncorrelated random initial conditions. The representation of the uncorrelated random initial state and also of the step function profile in terms of free fermions allows the calculation of time-dependent higher order correlation functions. We outline the procedure using a field theoretic approach.Comment: 26 pages, 1 Postscript figure, uses epsf.st

Length and time scale divergences at the magnetization-reversal transition in the Ising model

The divergences of both the length and time scales, at the magnetization- reversal transition in Ising model under a pulsed field, have been studied in the linearized limit of the mean field theory. Both length and time scales are shown to diverge at the transition point and it has been checked that the nature of the time scale divergence agrees well with the result obtained from the numerical solution of the mean field equation of motion. Similar growths in length and time scales are also observed, as one approaches the transition point, using Monte Carlo simulations. However, these are not of the same nature as the mean field case. Nucleation theory provides a qualitative argument which explains the nature of the time scale growth. To study the nature of growth of the characteristic length scale, we have looked at the cluster size distribution of the reversed spin domains and defined a pseudo-correlation length which has been observed to grow at the phase boundary of the transition.Comment: 9 pages Latex, 3 postscript figure

Directed diffusion of reconstituting dimers

We discuss dynamical aspects of an asymmetric version of assisted diffusion of hard core particles on a ring studied by G. I. Menon {\it et al.} in J. Stat Phys. {\bf 86}, 1237 (1997). The asymmetry brings in phenomena like kinematic waves and effects of the Kardar-Parisi-Zhang nonlinearity, which combine with the feature of strongly broken ergodicity, a characteristic of the model. A central role is played by a single nonlocal invariant, the irreducible string, whose interplay with the driven motion of reconstituting dimers, arising from the assisted hopping, determines the asymptotic dynamics and scaling regimes. These are investigated both analytically and numerically through sector-dependent mappings to the asymmetric simple exclusion process.Comment: 10 pages, 6 figures. Slight corrections, one added reference. To appear in J. Phys. Cond. Matt. (2007). Special issue on chemical kinetic

Modeling one-dimensional island growth with mass-dependent detachment rates

We study one-dimensional models of particle diffusion and attachment/detachment from islands where the detachment rates gamma(m) of particles at the cluster edges increase with cluster mass m. They are expected to mimic the effects of lattice mismatch with the substrate and/or long-range repulsive interactions that work against the formation of long islands. Short-range attraction is represented by an overall factor epsilon<<1 in the detachment rates relatively to isolated particle hopping rates [epsilon ~ exp(-E/T), with binding energy E and temperature T]. We consider various gamma(m), from rapidly increasing forms such as gamma(m) ~ m to slowly increasing ones, such as gamma(m) ~ [m/(m+1)]^b. A mapping onto a column problem shows that these systems are zero-range processes, whose steady states properties are exactly calculated under the assumption of independent column heights in the Master equation. Simulation provides island size distributions which confirm analytic reductions and are useful whenever the analytical tools cannot provide results in closed form. The shape of island size distributions can be changed from monomodal to monotonically decreasing by tuning the temperature or changing the particle density rho. Small values of the scaling variable X=epsilon^{-1}rho/(1-rho) favour the monotonically decreasing ones. However, for large X, rapidly increasing gamma(m) lead to distributions with peaks very close to and rapidly decreasing tails, while slowly increasing gamma(m) provide peaks close to /2$ and fat right tails.Comment: 16 pages, 6 figure

Sample-Dependent Phase Transitions in Disordered Exclusion Models

We give numerical evidence that the location of the first order phase transition between the low and the high density phases of the one dimensional asymmetric simple exclusion process with open boundaries becomes sample dependent when quenched disorder is introduced for the hopping rates.Comment: accepted in Europhysics Letter

Duality and phase diagram of one dimensional transport

The observation of duality by Mukherji and Mishra in one dimensional transport problems has been used to develop a general approach to classify and characterize the steady state phase diagrams. The phase diagrams are determined by the zeros of a set of coarse-grained functions without the need of detailed knowledge of microscopic dynamics. In the process, a new class of nonequilibrium multicritical points has been identified.Comment: 6 pages, 2 figures (4 eps files

Smoothly-varying hopping rates in driven flow with exclusion

We consider the one-dimensional totally asymmetric simple exclusion process (TASEP) with position-dependent hopping rates. The problem is solved,in a mean field/adiabatic approximation, for a general (smooth) form of spatial rate variation. Numerical simulations of systems with hopping rates varying linearly against position (constant rate gradient), for both periodic and open boundary conditions, provide detailed confirmation of theoretical predictions, concerning steady-state average density profiles and currents, as well as open-system phase boundaries, to excellent numerical accuracy.Comment: RevTeX 4.1, 14 pages, 9 figures (published version