Fluctuations and skewness of the current in the partially asymmetric exclusion process

Abstract

We use functional Bethe Ansatz equations to calculate the cumulants of the total current in the partially asymmetric exclusion process. We recover known formulas for the first two cumulants (mean value of the current and diffusion constant) and obtain an explicit finite size formula for the third cumulant. The expression for the third cumulant takes a simple integral form in the limit where the asymmetry scales as the inverse of the square root of the size of the system, which corresponds to a natural separation between weak and strong asymmetry.

arXiv comment21 pages, 3 figures

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Cited by in corpus (16)

• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Current large deviation function for the open asymmetric simple exclusion process
• Some Exact Results for the Exclusion Process
• Matrix product solution of the multispecies partially asymmetric exclusion process
• Cumulants of the current in the weakly asymmetric exclusion process
• Tree structures for the current fluctuations in the exclusion process
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice - bulk eigenvalues
• Equivalent T-Q relations and exact results for the open TASEP
• Assisted exchange models in one dimension
• Exact Large Deviations of the Current in the Asymmetric Simple Exclusion Process with Open Boundaries
• KPZ fluctuations in finite volume
• Current fluctuations in a partially asymmetric simple exclusion process with a defect particle
• From the Riemann surface of TASEP to ASEP
• A combinatorial solution for the current fluctuations in the exclusion process
• Mapping current and activity fluctuations in exclusion processes: consequences and open questions