Cluster-factorized steady states in finite-range processes

Chatterjee, Amit Kumar; Pradhan, Punyabrata; Mohanty, P. K.

doi:10.1103/physreve.92.032103

Cited by 8 publications

(59 citation statements)

References 29 publications

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“…Stochastic processes like ZRP, AZRP, MAP, AMAP constitute a specific class of non-equilibrium processes that enjoy the simplicity of FSS. But one can also have pair factorized steady state (PFSS) [12] and cluster factorized steady state (CFSS) [10] for generic models where particle interaction extends beyond departure and arrival sites. Such finite range processes (FRP) introduce spatial correlations among occupation at different sites leading to extended condensates.…”

Section: Asymmetric Finite Range Process Process (Afrp)mentioning

confidence: 99%

“…(10). For this choice of v(n), the model has three parameters b > 0, 0 < δ ≤ 1 and γ; here γ must be in the range 0…”

Section: Condensationmentioning

confidence: 99%

“…Like ZRP, misanthrope process can also have factorized steady state [11], but only for a certain class of hop rates. However, factorized steady state is not possible for FRP [10] where three or more sites are involved in the hop rates. For these systems, in fact, one can obtain a cluster factorized steady state (CFSS) when the rates satisfy certain specific conditions [10].…”

Section: Introductionmentioning

confidence: 99%

“…However, factorized steady state is not possible for FRP [10] where three or more sites are involved in the hop rates. For these systems, in fact, one can obtain a cluster factorized steady state (CFSS) when the rates satisfy certain specific conditions [10]. The simplest example of a cluster factorized steady state is a pair factorized state, introduced by Evans et.…”

Section: Introductionmentioning

confidence: 99%

“…A natural extension of ZRP is the finite range process (FRP), where the hop rate of the particles depends on the occupation number of not only the departure site but also that of all other sites within a specified distance [10]; clearly in FRP, particleparticle interaction extends to a finite number of neighboring lattice sites. A specific example, where the hop rate depends on occupation numbers of both the departure and the arrival sites, is commonly known as misanthrope process (MAP) [11].…”

Section: Introductionmentioning

confidence: 99%

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Zero range and finite range processes with asymmetric rate functions

Chatterjee

Mohanty

2017

J. Stat. Mech.

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Abstract. We introduce and solve exactly a class of interacting particle systems in one dimension where particles hop asymmetrically. In its simplest form, namely asymmetric zero range process (AZRP), particles hop on a one dimensional periodic lattice with asymmetric hop rates; the rates for both right and left moves depend only on the occupation at the departure site but their functional forms are different. We show that AZRP leads to a factorized steady state (FSS) when its rate-functions satisfy certain constraints. We demonstrate with explicit examples that AZRP exhibits certain interesting features which were not possible in usual zero range process. Firstly, it can undergo a condensation transition depending on how often a particle makes a right move compared to a left one and secondly, the particle current in AZRP can reverse its direction as density is changed. We show that these features are common in other asymmetric models which have FSS, like the asymmetric misanthrope process where rate functions for right and left hops are different, and depend on occupation of both the departure and the arrival site. We also derive sufficient conditions for having cluster-factorized steady states for finite range process with such asymmetric rate functions and discuss possibility of condensation there.Keywords: Zero-range processes, Non-equilibrium processes, Exact results Zero range and finite range processes with asymmetric rate functions 2

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Section: Asymmetric Finite Range Process Process (Afrp)mentioning

confidence: 99%

“…(10). For this choice of v(n), the model has three parameters b > 0, 0 < δ ≤ 1 and γ; here γ must be in the range 0…”

Section: Condensationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Zero range and finite range processes with asymmetric rate functions

Chatterjee

Mohanty

2017

J. Stat. Mech.

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Reentrant condensation transition in a two species driven diffusive system

Daga

2017

Physica A: Statistical Mechanics and its Applications

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We study an interacting box-particle system on a one-dimensional periodic ring involving two species of particles A and B. In this model, from a randomly chosen site, a particle of species A can hop to its right neighbor with a rate that depends on the number of particles of the species B at that site. On the other hand, particles of species B can be transferred between two neighboring sites with rates that depends on the number of particles of species B at the two adjacent sites−this process however can occur only when the two sites are devoid of particles of the species A. We study condensation transition for a specific choice of rates and find that the system shows a reentrant phase transition of species A − the species A passes successively through fluid-condensate-fluid phases as the coupling parameter between the dynamics of the two species is varied. On the other hand, the transition of species B is from condensate to fluid phase and hence does not show reentrant feature.

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Particle hopping on a ladder: exact solution using multibalance

Mukherjee¹

2021

J. Stat. Mech.

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We study particle hopping on a two-leg ladder where a particle can jump to their immediate neighbours, one at a time, with rates that depend on the occupation of the departure site and a neighbouring site on the other leg. For specific choices of rates, the model can be solved using pairwise balance known earlier. For the other regimes, we introduce a new balance condition called multibalance which helps us in obtaining the exact steady state. The direction of the total current in these models does not necessarily decide the direction of the currents in individual legs; we find the regions in the parameter space where the currents in individual legs alter their direction. In some parameter regime, the total current exhibits the re-entrance phenomena, in the sense that the total current flips its direction with increase of certain parameter and flips it again when the parameter is increased further. It turns out that the multibalance condition we introduce here is very useful and it can be applied generically to several other models. We discuss some of these models in short.

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Cluster-factorized steady states in finite-range processes

Cited by 8 publications

References 29 publications

Zero range and finite range processes with asymmetric rate functions

Zero range and finite range processes with asymmetric rate functions

Reentrant condensation transition in a two species driven diffusive system

Particle hopping on a ladder: exact solution using multibalance

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