Interaction-driven real-space condensation.

We study real-space condensation in a broad class of stochastic mass transport models. We show that the steady state of such models has a pair-factorized form which generalizes the standard factorized steady states. The condensation in this class of models is driven by interactions which give rise to a spatially extended condensate that differs fundamentally from the previously studied examples. We present numerical results as well as a theoretical analysis of the condensation transition and show that the criterion for condensation is related to the binding-unbinding transition of solid-on-solid interfaces.

Condensation transitions in a model for a directed network with weighted links.

An exactly solvable model for the rewiring dynamics of weighted, directed networks is introduced. Simulations indicate that the model exhibits two types of condensation: (i) a phase in which, for each node, a finite fraction of its total out-strength condenses onto a single link; (ii) a phase in which a finite fraction of the total weight in the system is directed into a single node. A virtue of the model is that its dynamics can be mapped onto those of a zero-range process with many species of interacting particles--an exactly solvable model of particles hopping between the sites of a lattice. This mapping, which is described in detail, guides the analysis of the steady state of the network model and leads to theoretical predictions for the conditions under which the different types of condensation may be observed. A further advantage of the mapping is that, by exploiting what is known about exactly solvable generalizations of the zero-range process, one can infer a number of generalizations of the network model and dynamics which remain exactly solvable.

Quantum scaling approach to nonequilibrium models.

Stochastic nonequilibrium exclusion models are treated using a real space scaling approach. The method exploits the mapping between nonequilibrium and quantum systems, and it is developed to accommodate conservation laws and duality symmetries, yielding exact fixed points for a variety of exclusion models. In addition, it is shown how the asymmetric simple exclusion process in one dimension can be written in terms of a classical Hamiltonian in two dimensions using a Suzuki-Trotter decomposition.

Coarsening dynamics in a two-species zero-range process.

We consider a zero-range process with two species of interacting particles. The steady-state phase diagram of this model shows a variety of condensate phases in which a single site contains a finite fraction of all the particles in the system. Starting from a homogeneous initial distribution, we study the coarsening dynamics in each of these condensate phases, which is expected to follow a scaling law. Random-walk arguments are used to predict the coarsening exponents in each condensate phase. They are shown to depend on the form of the hop rates and on the symmetry of the hopping dynamics. The analytic predictions are found to be in good agreement with the results of Monte Carlo simulations.

Condensation transitions in a two-species zero-range process.

We study condensation transitions in the steady state of a zero-range process with two species of particles. The steady state is exactly soluble-it is given by a factorized form provided the dynamics satisfy certain constraints-and we exploit this to derive the phase diagram for a quite general choice of dynamics. This phase diagram contains a variety of mechanisms of condensate formation, and a phase in which the condensate of one of the particle species is sustained by a "weak" condensate of particles of the other species. We also demonstrate how a single particle of one of the species (which plays the role of a defect particle) can induce Bose condensation above a critical density of particles of the other species.

Disorder and nonconservation in a driven diffusive system.

We consider a disordered asymmetric exclusion process in which randomly chosen sites do not conserve particle number. The model is motivated by features of many interacting molecular motors such as RNA polymerases. We solve the steady state exactly in the two limits of infinite and vanishing nonconserving rates. The first limit is used as an approximation to large but finite rates and allows the study of Griffiths singularities in a nonequilibrium steady state despite the absence of any transition in the pure model. The disorder is also shown to induce a stretched exponential decay of system density with stretching exponent phi=2/5 .