Symmetric Exclusion Process with a Localized Source

Abstract

We investigate the growth of the total number of particles in a symmetric exclusion process driven by a localized source. The average total number of particles entering an initially empty system grows with time as t^{1/2} in one dimension, t/log(t) in two dimensions, and linearly in higher dimensions. In one and two dimensions, the leading asymptotic behaviors for the average total number of particles are independent on the intensity of the source. We also discuss fluctuations of the total number of particles and determine the asymptotic growth of the variance in one dimension.

7 pages; small corrections, references added, final version

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Cited by in corpus (11)

• Survival of a static target in a gas of diffusing particles with exclusion
• Free Fermions with a Localized Source
• Free Bosons with a Localized Source
• The asymmetric simple exclusion process with an open boundary
• Current fluctuations in a semi-infinite line
• Lattice gases with a point source
• Full absorption statistics of diffusing particles with exclusion
• Semi-infinite simple exclusion process: from current fluctuations to target survival
• Scrambling Transition in Free Fermion Systems Induced by a Single Impurity
• Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond
• Random walk through a fertile site