43 research outputs found
Condensation in randomly perturbed zero-range processes
The zero-range process is a stochastic interacting particle system that
exhibits a condensation transition under certain conditions on the dynamics. It
has recently been found that a small perturbation of a generic class of jump
rates leads to a drastic change of the phase diagram and prevents condensation
in an extended parameter range. We complement this study with rigorous results
on a finite critical density and quenched free energy in the thermodynamic
limit, as well as quantitative heuristic results for small and large noise
which are supported by detailed simulation data. While our new results support
the initial findings, they also shed new light on the actual (limited)
relevance in large finite systems, which we discuss via fundamental diagrams
obtained from exact numerics for finite systems.Comment: 18 pages, 6 figure
Instability of condensation in the zero-range process with random interaction
The zero-range process is a stochastic interacting particle system that is
known to exhibit a condensation transition. We present a detailed analysis of
this transition in the presence of quenched disorder in the particle
interactions. Using rigorous probabilistic arguments we show that disorder
changes the critical exponent in the interaction strength below which a
condensation transition may occur. The local critical densities may exhibit
large fluctuations and their distribution shows an interesting crossover from
exponential to algebraic behaviour.Comment: 4 pages, 4 figures; included new simulation data (Fig. 4), small
changes in introduction and conclusio
Condensation in stochastic mass transport models: beyond the zero-range process
We consider an extension of the zero-range process to the case where the hop
rate depends on the state of both departure and arrival sites. We recover the
misanthrope and the target process as special cases for which the probability
of the steady state factorizes over sites. We discuss conditions which lead to
the condensation of particles and show that although two different hop rates
can lead to the same steady state, they do so with sharply contrasting
dynamics. The first case resembles the dynamics of the zero-range process,
whereas the second case, in which the hop rate increases with the occupation
number of both sites, is similar to instantaneous gelation models. This new
"explosive" condensation reveals surprisingly rich behaviour, in which the
process of condensate's formation goes through a series of collisions between
clusters of particles moving through the system at increasing speed. We perform
a detailed numerical and analytical study of the dynamics of condensation: we
find the speed of the moving clusters, their scattering amplitude, and their
growth time. We finally show that the time to reach steady state decreases with
the size of the system.Comment: 31 pages, 14 figures, submitted to J. Phys.
Condensation in models with factorized and pair-factorized stationary states
Non-equilibrium real-space condensation is a phenomenon in which a finite
fraction of some conserved quantity (mass, particles, etc.) becomes spatially
localised. We review two popular stochastic models of hopping particles that
lead to condensation and whose stationary states assume a factorized form: the
zero-range process and the misanthrope process, and their various
modifications. We also introduce a new model - a misanthrope process with
parallel dynamics - that exhibits condensation and has a pair-factorized
stationary state.Comment: 15 pages, 2 figures submitted to J. Stat. Mec