Finite-dimensional representation of the quadratic algebra of a generalized coagulation-decoagulation model

The steady-state of a generalized coagulation-decoagulation model on a one-dimensional lattice with reflecting boundaries is studied using a matrix-product approach. It is shown that the quadratic algebra of the model has a four-dimensional representation provided that some constraints on the microscopic reaction rates are fulfilled. The dynamics of a product shock measure with two shock fronts, generated by the Hamiltonian of this model, is also studied. It turns out that the shock fronts move on the lattice as two simple random walkers which repel each other provided that the same constraints on the microscopic reaction rates are satisfied.Comment: Minor revision

Phase transitions and correlations in the bosonic pair contact process with diffusion: Exact results

The variance of the local density of the pair contact process with diffusion (PCPD) is investigated in a bosonic description. At the critical point of the absorbing phase transition (where the average particle number remains constant) it is shown that for lattice dimension d>2 the variance exhibits a phase transition: For high enough diffusion constants, it asymptotically approaches a finite value, while for low diffusion constants the variance diverges exponentially in time. This behavior appears also in the density correlation function, implying that the correlation time is negative. Yet one has dynamical scaling with a dynamical exponent calculated to be z=2.Comment: 20 pages, 5 figure

Relaxation time in a non-conserving driven-diffusive system with parallel dynamics

We introduce a two-state non-conserving driven-diffusive system in one-dimension under a discrete-time updating scheme. We show that the steady-state of the system can be obtained using a matrix product approach. On the other hand, the steady-state of the system can be expressed in terms of a linear superposition Bernoulli shock measures with random walk dynamics. The dynamics of a shock position is studied in detail. The spectrum of the transfer matrix and the relaxation times to the steady-state have also been studied in the large-system-size limit.Comment: 10 page

Ergodicity breaking in one-dimensional reaction-diffusion systems

We investigate one-dimensional driven diffusive systems where particles may also be created and annihilated in the bulk with sufficiently small rate. In an open geometry, i.e., coupled to particle reservoirs at the two ends, these systems can exhibit ergodicity breaking in the thermodynamic limit. The triggering mechanism is the random motion of a shock in an effective potential. Based on this physical picture we provide a simple condition for the existence of a non-ergodic phase in the phase diagram of such systems. In the thermodynamic limit this phase exhibits two or more stationary states. However, for finite systems transitions between these states are possible. It is shown that the mean lifetime of such a metastable state is exponentially large in system-size. As an example the ASEP with the A0A--AAA reaction kinetics is analyzed in detail. We present a detailed discussion of the phase diagram of this particular model which indeed exhibits a phase with broken ergodicity. We measure the lifetime of the metastable states with a Monte Carlo simulation in order to confirm our analytical findings.Comment: 25 pages, 14 figures; minor alterations, typos correcte

Ageing in bosonic particle-reaction models with long-range transport

Ageing in systems without detailed balance is studied in bosonic contact and pair-contact processes with Levy diffusion. In the ageing regime, the dynamical scaling of the two-time correlation function and two-time response function is found and analysed. Exact results for non-equilibrium exponents and scaling functions are derived. The behaviour of the fluctuation-dissipation ratio is analysed. A passage time from the quasi-stationary regime to the ageing regime is defined, in qualitative agreement with kinetic spherical models and p-spin spherical glasses.Comment: Latex2e, 24 pages, with 9 figures include

Dynamics of an exclusion process with creation and annihilation

We examine the dynamical properties of an exclusion process with creation and annihilation of particles in the framework of a phenomenological domain-wall theory, by scaling arguments and by numerical simulation. We find that the length- and time scale are finite in the maximum current phase for finite creation- and annihilation rates as opposed to the algebraically decaying correlations of the totally asymmetric simple exclusion process (TASEP). Critical exponents of the transition to the TASEP are determined. The case where bulk creation- and annihilation rates vanish faster than the inverse of the system size N is also analyzed. We point out that shock localization is possible even for rates proportional to 1/N^a, 1<a<2.Comment: 16 pages, 8 figures, typos corrected, references added, section 4 revise

The non-equilibrium phase transition of the pair-contact process with diffusion

The pair-contact process 2A->3A, 2A->0 with diffusion of individual particles is a simple branching-annihilation processes which exhibits a phase transition from an active into an absorbing phase with an unusual type of critical behaviour which had not been seen before. Although the model has attracted considerable interest during the past few years it is not yet clear how its critical behaviour can be characterized and to what extent the diffusive pair-contact process represents an independent universality class. Recent research is reviewed and some standing open questions are outlined.Comment: Latexe2e, 53 pp, with IOP macros, some details adde

Microscopic structure of travelling wave solutions in a class of stochastic interacting particle systems

We obtain exact travelling wave solutions for three families of stochastic one-dimensional nonequilibrium lattice models with open boundaries. These solutions describe the diffusive motion and microscopic structure of (i) of shocks in the partially asymmetric exclusion process with open boundaries, (ii) of a lattice Fisher wave in a reaction-diffusion system, and (iii) of a domain wall in non-equilibrium Glauber-Kawasaki dynamics with magnetization current. For each of these systems we define a microscopic shock position and calculate the exact hopping rates of the travelling wave in terms of the transition rates of the microscopic model. In the steady state a reversal of the bias of the travelling wave marks a first-order non-equilibrium phase transition, analogous to the Zel'dovich theory of kinetics of first-order transitions. The stationary distributions of the exclusion process with $n$ shocks can be described in terms of $n$-dimensional representations of matrix product states.Comment: 27 page

Exchange anisotropy and the dynamic phase transition in thin ferromagnetic Heisenberg films

Monte Carlo simulations have been performed to investigate the dependence of the dynamic phase behavior on the bilinear exchange anisotropy of a classical Heisenberg spin system. The system under consideration is a planar thin ferromagnetic film with competing surface fields subject to a pulsed oscillatory external field. The results show that the films exhibit a single discontinuous dynamic phase transition (DPT) as a function of the anisotropy of the bilinear exchange interaction in the Hamiltonian. Furthermore there is no evidence of stochastic resonance (SR) associated with the DPT. These results are in marked contrast to the continuous DPT observed in the same system as a function of temperature and applied field strength for a fixed bilinear exchange anisotropy.Comment: 11 pages including 3 figure pages; submitted to PR

The kinetic spherical model in a magnetic field

The long-time kinetics of the spherical model in an external magnetic field and below the equilibrium critical temperature is studied. The solution of the associated stochastic Langevin equation is reduced exactly to a single non-linear Volterra equation. For a sufficiently small external field, the kinetics of the magnetization-reversal transition from the metastable to the ground state is compared to the ageing behaviour of coarsening systems quenched into the low-temperature phase. For an oscillating magnetic field and below the critical temperature, we find evidence for the absence of the frequency-dependent dynamic phase transition, which was observed previously to occur in Ising-like systems.Comment: 26 pages, 12 figure