Zero-range process with finite compartments: Gentile's statistics and glassiness

Ryabov, Artem

doi:10.1103/physreve.89.022115

Cited by 6 publications

(6 citation statements)

References 37 publications

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“…Generalized exclusion processes (GEPs) with maximal occupation number 1 < k < ∞ have been studied in [20][21][22]; see also Refs. [23][24][25][26][27][28][29][30][31][32][33] for other versions of GEPs. Some of these models can be mapped onto multi-species exclusion processes [34][35][36] but with nonconserving species.…”

Section: Classical Lattice Gases)mentioning

confidence: 99%

Generalized exclusion processes: Transport coefficients

2014

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A class of generalized exclusion processes with symmetric nearest-neighbor hopping which are parametrized by the maximal occupancy, k ≥ 1, is investigated. For these processes on hyper-cubic lattices we compute the diffusion coefficient in all spatial dimensions. In the extreme cases of k = 1 (symmetric simple exclusion process) and k = ∞ (non-interacting symmetric random walks) the diffusion coefficient is constant, while for 2 ≤ k < ∞ it depends on the density and k. We also study the evolution of the tagged particle, show that it exhibits a normal diffusive behavior in all dimensions, and probe numerically the coefficient of self-diffusion.

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Section: Classical Lattice Gases)mentioning

confidence: 99%

Generalized exclusion processes: Transport coefficients

2014

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“…Some relevant open questions still lay ahead; one, in particular, concerns the existence of phase transitions and stationary currents when considering different geometries of the channels and/or of the cavities, or by adding longrange particle interactions. Further challenging mathematical questions concern the investigation of the thermodynamic limit of our model, the relaxation of the par-ticle system toward a nonequilibrium steady state, which could even exhibit anomalous behavior [31], and applications to the modelling of physical and chemical kinetics.…”

Section: Discussionmentioning

confidence: 99%

Deterministic model of battery, uphill currents and non-equilibrium phase transitions

Cirillo,

Colangeli,

Richardson

et al. 2021

Preprint

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We consider point particles in a table made of two circular cavities connected by two rectangular channels, forming a closed loop under periodic boundary conditions. In the first channel, a bounceback mechanism acts when the number of particles flowing in one direction exceeds a given threshold T . In that case, the particles invert their horizontal velocity, as if colliding with vertical walls. The second channel is divided in two halves parallel to the first, but located in the opposite sides of the cavities. In the second channel, motion is free. We show that, suitably tuning the sizes of cavities, of the channels and of T , non-equilibrium phase transitions take place in the N → ∞ limit. This induces a stationary current in the circuit, thus modeling a kind of battery, although our model is deterministic, conservative, and time reversal invariant.

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“…Using the mapping between EP and ZRP described in Sec. II and summing over all the particle configurations in front of the ith and (i + r)th particle, we get where we have used (14) to arrive at the last expression. As the total number of particles is conserved, the maximum number of particles in the first cluster can be N −1.…”

Section: Two-point Correlation Function In Canonical Ensemblementioning

confidence: 99%

“…The ZRP, in which a particle hops to a neighbouring site with a rate that depends only on the properties of the departure site, has the attractive feature that its steady state distribution can be found exactly [6]. This model has been generalised in various directions in recent years [7][8][9], and has been used to model clustering phenomena in traffic flow [10], granular gases [11] and networks [12], avalanche dynamics in sandpiles [13], slow dynamics in glasses [14], and to understand phase separation in nonequilibrium systems [15].…”

Section: Introductionmentioning

confidence: 99%

Two-point correlation function of an exclusion process with hole-dependent rates

2014

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We consider an exclusion process on a ring in which a particle hops to an empty neighbouring site with a rate that depends on the number of vacancies n in front of it. In the steady state, using the well known mapping of this model to the zero range process, we write down an exact formula for the partition function and the particle-particle correlation function in the canonical ensemble. In the thermodynamic limit, we find a simple analytical expression for the generating function of the correlation function. This result is applied to the hop rate u(n) = 1 + (b/n) for which a phase transition between high-density laminar phase and low-density jammed phase occurs for b > 2. For these rates, we find that at the critical density, the correlation function decays algebraically with a continuously varying exponent b − 2. We also calculate the two-point correlation function above the critical density, and find that the correlation length diverges with a critical exponent ν = 1/(b − 2) for b < 3 and 1 for b > 3. These results are compared with those obtained using an exact series expansion for finite systems.

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Zero-range process with finite compartments: Gentile's statistics and glassiness

Cited by 6 publications

References 37 publications

Generalized exclusion processes: Transport coefficients

Generalized exclusion processes: Transport coefficients

Deterministic model of battery, uphill currents and non-equilibrium phase transitions

Two-point correlation function of an exclusion process with hole-dependent rates

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