Bethe ansatz solution of zero-range process with nonuniform stationary state

The eigenfunctions and eigenvalues of the master-equation for zero range process with totally asymmetric dynamics on a ring are found exactly using the Bethe ansatz weighted with the stationary weights of particle configurations. The Bethe ansatz applicability requires the rates of hopping of particles out of a site to be the $q$-numbers $[n]_q$. This is a generalization of the rates of hopping of noninteracting particles equal to the occupation number $n$ of a site of departure. The noninteracting case can be restored in the limit $q\to 1$. The limiting cases of the model for $q=0,\infty$ correspond to the totally asymmetric exclusion process, and the drop-push model respectively. We analyze the partition function of the model and apply the Bethe ansatz to evaluate the generating function of the total distance travelled by particles at large time in the scaling limit. In case of non-zero interaction, $q \ne 1$, the generating function has the universal scaling form specific for the Kardar-Parizi-Zhang universality class.Comment: 7 pages, Revtex4, mistypes correcte

Asymmetric exclusion processes with constrained dynamics

Asymmetric exclusion processes with locally reversible kinetic constraints are introduced to investigate the effect of non-conservative driving forces in athermal systems. At high density they generally exhibit rheological-like behavior, negative differential resistance, two-step structural relaxation, dynamical heterogeneity and, possibly, a jamming transition driven by the external field.Comment: 4 pages, 4 figures; revised version: minor changes, added references; to be publishe

Infinite reflections of shock fronts in driven diffusive systems with two species

Interaction of a domain wall with boundaries of a system is studied for a class of stochastic driven particle models. Reflection maps are introduced for the description of this process. We show that, generically, a domain wall reflects infinitely many times from the boundaries before a stationary state can be reached. This is in an evident contrast with one-species models where the stationary density is attained after just one reflection.Comment: 11 pages, 8 eps figs, to appearin JPhysA 01.200

Phase Coexistence in Driven One Dimensional Transport

We study a one-dimensional totally asymmetric exclusion process with random particle attachments and detachments in the bulk. The resulting dynamics leads to unexpected stationary regimes for large but finite systems. Such regimes are characterized by a phase coexistence of low and high density regions separated by domain walls. We use a mean-field approach to interpret the numerical results obtained by Monte-Carlo simulations and we predict the phase diagram of this non-conserved dynamics in the thermodynamic limit.Comment: 4 pages, 3 figures. Accepted for publication on Phys. Rev. Let

Spontaneous Symmetry Breaking in a Non-Conserving Two-Species Driven Model

A two species particle model on an open chain with dynamics which is non-conserving in the bulk is introduced. The dynamical rules which define the model obey a symmetry between the two species. The model exhibits a rich behavior which includes spontaneous symmetry breaking and localized shocks. The phase diagram in several regions of parameter space is calculated within mean-field approximation, and compared with Monte-Carlo simulations. In the limit where fluctuations in the number of particles in the system are taken to zero, an exact solution is obtained. We present and analyze a physical picture which serves to explain the different phases of the model

Why spontaneous symmetry breaking disappears in a bridge system with PDE-friendly boundaries

We consider a driven diffusive system with two types of particles, A and B, coupled at the ends to reservoirs with fixed particle densities. To define stochastic dynamics that correspond to boundary reservoirs we introduce projection measures. The stationary state is shown to be approached dynamically through an infinite reflection of shocks from the boundaries. We argue that spontaneous symmetry breaking observed in similar systems is due to placing effective impurities at the boundaries and therefore does not occur in our system. Monte-Carlo simulations confirm our results.Comment: 24 pages, 7 figure

Hydrodynamics of the zero-range process in the condensation regime

We argue that the coarse-grained dynamics of the zero-range process in the condensation regime can be described by an extension of the standard hydrodynamic equation obtained from Eulerian scaling even though the system is not locally stationary. Our result is supported by Monte Carlo simulations.Comment: 14 pages, 3 figures. v2: Minor alteration

Finite-size effects on the dynamics of the zero-range process

We study finite-size effects on the dynamics of a one-dimensional zero-range process which shows a phase transition from a low-density disordered phase to a high-density condensed phase. The current fluctuations in the steady state show striking differences in the two phases. In the disordered phase, the variance of the integrated current shows damped oscillations in time due to the motion of fluctuations around the ring as a dissipating kinematic wave. In the condensed phase, this wave cannot propagate through the condensate, and the dynamics is dominated by the long-time relocation of the condensate from site to site.Comment: 5 pages, 5 figures, version published in Phys. Rev. E Rapid Communication

Comment on "Systematics of the Induced Magnetic Moments in 5d Layers and the Violation of the Third Hund's Rule"

Comment on F. Wilhelm et al., Phys. Rev. Lett. 87, 207202 (2001)Comment: 1 pag

Weakly disordered absorbing-state phase transitions

The effects of quenched disorder on nonequilibrium phase transitions in the directed percolation universality class are revisited. Using a strong-disorder energy-space renormalization group, it is shown that for any amount of disorder the critical behavior is controlled by an infinite-randomness fixed point in the universality class of the random transverse-field Ising models. The experimental relevance of our results are discussed.Comment: 4 pages, 2 eps figures; (v2) references and discussion on experiments added; (v3) published version, minor typos corrected, some side discussions dropped due to size constrain