Current Fluctuations in the exclusion process and Bethe Ansatz

Abstract

We use the Bethe Ansatz to derive analytical expressions for the current statistics in the asymmetric exclusion process with both forward and backward jumps. The Bethe equations are highly coupled and this fact has impeded their use to derive exact results for finite systems. We overcome this technical difficulty by a reformulation of the Bethe equations into a one variable polynomial problem, akin to the functional Bethe Ansatz. The perturbative solution of this equation leads to the cumulants of the current. We calculate here the first two orders and derive exact formulae for the mean value of the current and its fluctuations.

17 pages

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Cited by in corpus (34)

• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Universal cumulants of the current in diffusive systems on a ring
• Current Fluctuations in One Dimensional Diffusive Systems with a Step Initial Density Profile
• Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition
• Logarithmic current fluctuations in non-equilibrium quantum spin chains
• Fluctuations of Current in Non-Stationary Diffusive Lattice Gases
• Dynamical symmetry breaking and phase transitions in driven diffusive systems
• Large deviations and dynamical phase transitions in stochastic chemical networks
• Current fluctuations in non-interacting run-and-tumble particles in one-dimension
• Some Exact Results for the Exclusion Process
• Matrix product solution of the multispecies partially asymmetric exclusion process
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• Dynamical phase behavior of the single- and multi-lane asymmetric simple exclusion process via matrix product states
• Cumulants of the current in the weakly asymmetric exclusion process
• Tree structures for the current fluctuations in the exclusion process
• Fluctuations and skewness of the current in the partially asymmetric exclusion process
• Current fluctuations in stochastically resetting particle systems
• Effusion of stochastic processes on a line
• Asymmetric exclusion processes with fixed resources: Reservoir crowding and steady states
• Large deviations in the symmetric simple exclusion process with slow boundaries
• Efficiency of one-dimensional active transport conditioned on motility
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• Assisted exchange models in one dimension
• Integrability of two-species partially asymmetric exclusion processes
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• KPZ fluctuations in finite volume
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