Large deviation functions in a system of diffusing particles with creation and annihilation

Large deviation functions for an exactly solvable lattice gas model of diffusing particles on a ring, subject to pair annihilation and creation, are obtained analytically using exact free-fermion techniques. Our findings for the large deviation function for the current are compared to recent results of Appert-Rolland et al. [Phys. Rev. E 78, 021122 (2008)] for diffusive systems with conserved particle number. Unlike conservative dynamics, our nonconservative model has no universal finite-size corrections for the cumulants. However, the leading Gaussian part has the same variance as in the conservative case. We also elucidate some properties of the large deviation functions associated with particle creation and annihilation

Unusual shock wave in two-species driven systems with an umbilic point

Using dynamical Monte Carlo simulations we observe the occurrence of an unexpected shock wave in driven diffusive systems with two conserved species of particles. This U shock is microscopically sharp, but does not satisfy the usual criteria for the stability of shocks. Exact analysis of the large-scale hydrodynamic equations of motion reveals the presence of an umbilical point which we show to be responsible for this phenomenon. We prove that such an umbilical point is a general feature of multispecies driven diffusive systems with reflection symmetry of the bulk dynamics. We argue that a U shock will occur whenever there are strong interactions between species such that the current-density relation develops a double well and the umbilical point becomes isolated

Solution of a class of one-dimensional reaction-diffusion models in disordered media

We study a one-dimensional class of reaction-diffusion models on a $10-$parameters manifold. The equations of motion of the correlation functions close on this manifold. We compute exactly the long-time behaviour of the density and correlation functions for {\it quenched} disordered systems. The {\it quenched} disorder consists of disconnected domains of reaction. We first consider the case where the disorder comprizes a superposition, with different probabilistic weights, of finite segments, with {\it periodic boundary conditions}. We then pass to the case of finite segments with {\it open boundary conditions}: we solve the ordered dynamics on a open lattice with help of the Dynamical Matrix Ansatz (DMA) and investigate further its disordered version.Comment: 11 pages, no figures. To appear in Phys.Rev.

On the solvable multi-species reaction-diffusion processes

A family of one-dimensional multi-species reaction-diffusion processes on a lattice is introduced. It is shown that these processes are exactly solvable, provided a nonspectral matrix equation is satisfied. Some general remarks on the solutions to this equation, and some special solutions are given. The large-time behavior of the conditional probabilities of such systems are also investigated.Comment: 13 pages, LaTeX2

Exact time-dependent correlation functions for the symmetric exclusion process with open boundary

As a simple model for single-file diffusion of hard core particles we investigate the one-dimensional symmetric exclusion process. We consider an open semi-infinite system where one end is coupled to an external reservoir of constant density $\rho^\ast$ and which initially is in an non-equilibrium state with bulk density $\rho_0$. We calculate the exact time-dependent two-point density correlation function $C_{k,l}(t)\equiv -$ and the mean and variance of the integrated average net flux of particles $N(t)-N(0)$ that have entered (or left) the system up to time $t$. We find that the boundary region of the semi-infinite relaxing system is in a state similar to the bulk state of a finite stationary system driven by a boundary gradient. The symmetric exclusion model provides a rare example where such behavior can be proved rigorously on the level of equal-time two-point correlation functions. Some implications for the relaxational dynamics of entangled polymers and for single-file diffusion in colloidal systems are discussed.Comment: 11 pages, uses REVTEX, 2 figures. Minor typos corrected and reference 17 adde

Solution of a one-dimensional stochastic model with branching and coagulation reactions

We solve an one-dimensional stochastic model of interacting particles on a chain. Particles can have branching and coagulation reactions, they can also appear on an empty site and disappear spontaneously. This model which can be viewed as an epidemic model and/or as a generalization of the {\it voter} model, is treated analytically beyond the {\it conventional} solvable situations. With help of a suitably chosen {\it string function}, which is simply related to the density and the non-instantaneous two-point correlation functions of the particles, exact expressions of the density and of the non-instantaneous two-point correlation functions, as well as the relaxation spectrum are obtained on a finite and periodic lattice.Comment: 5 pages, no figure. To appear as a Rapid Communication in Physical Review E (September 2001

Spectral Degeneracies in the Totally Asymmetric Exclusion Process

We study the spectrum of the Markov matrix of the totally asymmetric exclusion process (TASEP) on a one-dimensional periodic lattice at ARBITRARY filling. Although the system does not possess obvious symmetries except translation invariance, the spectrum presents many multiplets with degeneracies of high order. This behaviour is explained by a hidden symmetry property of the Bethe Ansatz. Combinatorial formulae for the orders of degeneracy and the corresponding number of multiplets are derived and compared with numerical results obtained from exact diagonalisation of small size systems. This unexpected structure of the TASEP spectrum suggests the existence of an underlying large invariance group. Keywords: ASEP, Markov matrix, Bethe Ansatz, Symmetries.Comment: 19 pages, 1 figur

DMRG studies of the effect of constraint release on the viscosity of polymer melts

The scaling of the viscosity of polymer melts is investigated with regard to the molecular weight. We present a generalization of the Rubinstein-Duke model, which takes constraint releases into account and calculate the effects on the viscosity by the use of the Density Matrix Renormalization Group (DMRG) algorithm. Using input from Rouse theory the rates for the constraint release are determined in a self consistent way. We conclude that shape fluctuations of the tube caused by constraint release are not a likely candidate for improving Doi's crossover theory for the scaling of the polymer viscosity.Comment: 6 pages, 8 figure

Current moments of 1D ASEP by duality

We consider the exponential moments of integrated currents of 1D asymmetric simple exclusion process using the duality found by Sch\"utz. For the ASEP on the infinite lattice we show that the $n$th moment is reduced to the problem of the ASEP with less than or equal to $n$ particles.Comment: 13 pages, no figur

Determinant representation for some transition probabilities in the TASEP with second class particles

We study the transition probabilities for the totally asymmetric simple exclusion process (TASEP) on the infinite integer lattice with a finite, but arbitrary number of first and second class particles. Using the Bethe ansatz we present an explicit expression of these quantities in terms of the Bethe wave function. In a next step it is proved rigorously that this expression can be written in a compact determinantal form for the case where the order of the first and second class particles does not change in time. An independent geometrical approach provides insight into these results and enables us to generalize the determinantal solution to the multi-class TASEP.Comment: Minor revision; journal reference adde