Criticality and Condensation in a Non-Conserving Zero Range Process

The Zero-Range Process, in which particles hop between sites on a lattice under conserving dynamics, is a prototypical model for studying real-space condensation. Within this model the system is critical only at the transition point. Here we consider a non-conserving Zero-Range Process which is shown to exhibit generic critical phases which exist in a range of creation and annihilation parameters. The model also exhibits phases characterised by mesocondensates each of which contains a subextensive number of particles. A detailed phase diagram, delineating the various phases, is derived.Comment: 15 pages, 4 figure, published versi

Product Measure Steady States of Generalized Zero Range Processes

We establish necessary and sufficient conditions for the existence of factorizable steady states of the Generalized Zero Range Process. This process allows transitions from a site $i$ to a site $i+q$ involving multiple particles with rates depending on the content of the site $i$, the direction $q$ of movement, and the number of particles moving. We also show the sufficiency of a similar condition for the continuous time Mass Transport Process, where the mass at each site and the amount transferred in each transition are continuous variables; we conjecture that this is also a necessary condition.Comment: 9 pages, LaTeX with IOP style files. v2 has minor corrections; v3 has been rewritten for greater clarit

Slow Coarsening in a Class of Driven Systems

The coarsening process in a class of driven systems is studied. These systems have previously been shown to exhibit phase separation and slow coarsening in one dimension. We consider generalizations of this class of models to higher dimensions. In particular we study a system of three types of particles that diffuse under local conserving dynamics in two dimensions. Arguments and numerical studies are presented indicating that the coarsening process in any number of dimensions is logarithmically slow in time. A key feature of this behavior is that the interfaces separating the various growing domains are smooth (well approximated by a Fermi function). This implies that the coarsening mechanism in one dimension is readily extendible to higher dimensions.Comment: submitted to EPJB, 13 page

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

An exactly solvable dissipative transport model

We introduce a class of one-dimensional lattice models in which a quantity, that may be thought of as an energy, is either transported from one site to a neighbouring one, or locally dissipated. Transport is controlled by a continuous bias parameter q, which allows us to study symmetric as well as asymmetric cases. We derive sufficient conditions for the factorization of the N-body stationary distribution and give an explicit solution for the latter, before briefly discussing physically relevant situations.Comment: 7 pages, 1 figure, submitted to J. Phys.

Making Memories: Why Time Matters

In the last decade advances in human neuroscience have identified the critical importance of time in creating long-term memories. Circadian neuroscience has established biological time functions via cellular clocks regulated by photosensitive retinal ganglion cells and the suprachiasmatic nuclei. Individuals have different circadian clocks depending on their chronotypes that vary with genetic, age, and sex. In contrast, social time is determined by time zones, daylight savings time, and education and employment hours. Social time and circadian time differences can lead to circadian desynchronization, sleep deprivation, health problems, and poor cognitive performance. Synchronizing social time to circadian biology leads to better health and learning, as demonstrated in adolescent education. In-day making memories of complex bodies of structured information in education is organized in social time and uses many different learning techniques. Research in the neuroscience of long-term memory (LTM) has demonstrated in-day time spaced learning patterns of three repetitions of information separated by two rest periods are effective in making memories in mammals and humans. This time pattern is based on the intracellular processes required in synaptic plasticity. Circadian desynchronization, sleep deprivation, and memory consolidation in sleep are less well-understood, though there has been considerable progress in neuroscience research in the last decade. The interplay of circadian, in-day and sleep neuroscience research are creating an understanding of making memories in the first 24-h that has already led to interventions that can improve health and learning

Factorised Steady States in Mass Transport Models on an Arbitrary Graph

We study a general mass transport model on an arbitrary graph consisting of $L$ nodes each carrying a continuous mass. The graph also has a set of directed links between pairs of nodes through which a stochastic portion of mass, chosen from a site-dependent distribution, is transported between the nodes at each time step. The dynamics conserves the total mass and the system eventually reaches a steady state. This general model includes as special cases various previously studied models such as the Zero-range process and the Asymmetric random average process. We derive a general condition on the stochastic mass transport rules, valid for arbitrary graph and for both parallel and random sequential dynamics, that is sufficient to guarantee that the steady state is factorisable. We demonstrate how this condition can be achieved in several examples. We show that our generalized result contains as a special case the recent results derived by Greenblatt and Lebowitz for $d$-dimensional hypercubic lattices with random sequential dynamics.Comment: 17 pages 1 figur

Rules for transition rates in nonequilibrium steady states

Just as transition rates in a canonical ensemble must respect the principle of detailed balance, constraints exist on transition rates in driven steady states. I derive those constraints, by maximum information-entropy inference, and apply them to the steady states of driven diffusion and a sheared lattice fluid. The resulting ensemble can potentially explain nonequilibrium phase behaviour and, for steady shear, gives rise to stress-mediated long-range interactions.Comment: 4 pages. To appear in Physical Review Letter