Mean-field treatment of exclusion processes with random-force disorder

Self Cite

Abstract. We study coarsening phenomena in three different simple exclusion processes with quenched disordered jump rates. In the case of the totally asymmetric process, an earlier phenomenological description is improved, yielding for the time dependence of the length scale ξ(t) ∼ t/(ln t) 2 , which is found to be in agreement with results of Monte Carlo simulations. For the partially asymmetric process, the logarithmically slow coarsening predicted by a phenomenological theory is confirmed by Monte Carlo simulations and numerical mean-field calculations. Finally, coarsening in a bidirectional, two-lane model with random lane-change rates is studied. Here, Monte Carlo simulations indicate an unusual dependence of the dynamical exponent on the density of particles.

Section: Coarsening In the Disordered Partially Asymmetric Exclusion ...supporting

confidence: 58%

Section: Coarsening In the Disordered Partially Asymmetric Exclusion ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Anomalous coarsening in disordered exclusion processes

Juhász¹,

Ódor²

2012

Self Cite

“…The pure Simple Symmetric Exclusion Process with uniform D k,k+1 = 1 is one of the standard model in the field of non-equilibrium classical systems (see the review [34] and references therein). The effects of quenched disorder on totally or partially asymmetric exclusion models have been analyzed in [54][55][56][57][58]. In our present case, it is very important to stress that the disorder is in the local diffusion coefficients D k,k+1 , but that the symmetry between the jumps from k to (k + 1) or from (k + 1) to k is maintained.…”

Section: H Summary : Mapping Onto a Classical Exclusion Process With ...mentioning

confidence: 98%

“…In our present case, it is very important to stress that the disorder is in the local diffusion coefficients D k,k+1 , but that the symmetry between the jumps from k to (k + 1) or from (k + 1) to k is maintained. On the contrary, for the model with random hopping rates that do not satisfy this symmetry, there exists a random local force that build a random potential landscape with large barriers that will govern the transport properties [56][57][58], so that the physics is completely different.…”

Section: H Summary : Mapping Onto a Classical Exclusion Process Withmentioning

confidence: 99%

Dissipative random quantum spin chain with boundary-driving and bulk-dephasing: magnetization and current statistics in the non-equilibrium-steady-state

Monthus¹

2017

The Lindblad dynamics with dephasing in the bulk and magnetization-driving at the two boundaries is studied for the quantum spin chain with random fields hj and couplings Jj (that can be either uniform or random). In the regime of strong disorder in the random fields, or in the regime of strong bulk-dephasing, the effective dynamics can be mapped onto a classical Simple Symmetric Exclusion Process with quenched disorder in the diffusion coefficient associated to each bond. The properties of the corresponding Non-Equilibrium-Steady-State in each disordered sample between the two reservoirs are studied in detail by extending the methods that have been previously developed for the Symmetric Exclusion Process without disorder. Explicit results are given for the magnetization profile, for the two-point correlations, for the mean current and for the current fluctuations, in terms of the random fields and couplings defining the disordered sample.

Inhomogeneous asymmetric exclusion processes between two reservoirs: large deviations for the local empirical observables in the mean-field approximation

Monthus¹

2021

For a given inhomogeneous exclusion processes on N sites between two reservoirs, the trajectories probabilities allow to identify the relevant local empirical observables and to obtain the corresponding rate function at level 2.5. In order to close the hierarchy of the empirical dynamics that appear in the stationarity constraints, we consider the simplest approximation, namely the mean-field approximation for the empirical density of two consecutive sites, in direct correspondence with the previously studied mean-field approximation for the steady state. For a given inhomogeneous totally asymmetric model, this mean-field approximation yields the large deviations for the joint distribution of the empirical density profile and of the empirical current around the mean-field steady state; the further explicit contraction over the current allows to obtain the large deviations of the empirical density profile alone. For a given inhomogeneous asymmetric model, the local empirical observables also involve the empirical activities of the links and of the reservoirs; the further explicit contraction over these activities yields the large deviations for the joint distribution of the empirical density profile and of the empirical current. The consequences for the large deviations properties of time-additive space-local observables are also discussed in both cases.