Dynamics of condensation in zero-range processes

We study a one dimensional nonequilibrium lattice model with competing features of particle attraction and non-local hops. The system is similar to a zero range process (ZRP) with attractive particles but the particles can make both local and non-local hops. The length of the non-local hop is dependent on the occupancy of the chosen site and its probability is given by the parameter $p$. Our numerical results show that the system undergoes a phase transition from a condensate...

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 factorised 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 new mechanisms of condensate formation, and a novel phase in which the condensate of one of the particle species is s...

Condensation phenomena in particle systems typically occur as one of two distinct types: either as a spontaneous symmetry breaking in a homogeneous system, in which particle interactions enforce condensation in a randomly located site, or as an explicit symmetry breaking in a system with background disorder, in which particles condensate in the site of extremal disorder. In this paper we confirm a recent conjecture by Godr\`eche and Luck by showing, for a zero range process w...

Condensation occurs in nonequilibrium steady states when a finite fraction of particles in the system occupies a single lattice site. We study condensation transitions in a one-dimensional zero-range process with a single defect site. The system is analysed in the grand canonical and canonical ensembles and the two are contrasted. Two distinct condensation mechanisms are found in the grand canonical ensemble. Discrepancies between the infinite and large but finite systems' pa...

We consider the dynamics of the disordered, one-dimensional, symmetric zero range process in which a particle from an occupied site $k$ hops to its nearest neighbour with a quenched rate $w(k)$. These rates are chosen randomly from the probability distribution $f(w) \sim (w-c)^{n}$, where $c$ is the lower cutoff. For $n > 0$, this model is known to exhibit a phase transition in the steady state from a low density phase with a finite number of particles at each site to a high ...

We study a zero range process on scale-free networks in order to investigate how network structure influences particle dynamics. The zero range process is defined with the particle jumping rate function $p(n)=n^\delta$. We show analytically that a complete condensation occurs when $\delta \leq \delta_c \equiv 1/(\gamma-1)$ where $\gamma$ is the degree distribution exponent of the underlying networks. In the complete condensation, those nodes whose degree is higher than a thre...

The dynamics of zero-range processes on complex networks is expected to be influenced by the topological structure of underlying networks. A real space complete condensation phase transition in the stationary state may occur. We have studied the finite density effects of the condensation transition in both the stationary and dynamical zero-range process on scale-free networks. By means of grand canonical ensemble method, we predict analytically the scaling laws of the average...

We study the condensation phenomenon in a zero range process on weighted scale-free networks in order to show how the weighted transport influences the particle condensation. Instead of the approach of grand canonical ensemble which is generally used in a zero range process, we introduce an alternate approach of the mean field equations to study the dynamics of particle transport. We find that the condensation on scale-free network is easier to occur in the case of weighted t...

Driven diffusive systems such as the zero-range process (ZRP) and the pair-factorized steady states (PFSS) stochastic transport process are versatile tools that lend themselves to the study of transport phenomena on a generic level. While their mathematical structure is simple enough to allow significant analytical treatment, they offer a variety of interesting phenomena. With appropriate dynamics, the ZRP and PFSS models feature a condensation transition where for a supercri...

A free zero-range process (FRZP) is a simple stochastic process describing the dynamics of a gas of particles hopping between neighboring nodes of a network. We discuss three different cases of increasing complexity: (a) FZRP on a rigid geometry where the network is fixed during the process, (b) FZRP on a random graph chosen from a given ensemble of networks, (c) FZRP on a dynamical network whose topology continuously changes during the process in a way which depends on the c...