Tree structures for the current fluctuations in the exclusion process

Abstract

We consider the asymmetric simple exclusion process on a ring, with an arbitrary asymmetry between the hopping rates of the particles. Using a functional formulation of the Bethe equations of the model, we derive exact expressions for all the cumulants of the current in the stationary state. These expressions involve tree structures with composite nodes. In the thermodynamic limit, three regimes can be observed for the current fluctuations depending on how the asymmetry scales with the size of the system.

43 pages

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Cited by in corpus (30)

• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Exact Current Statistics of the ASEP with Open Boundaries
• The Exclusion Process: A paradigm for non-equilibrium behaviour
• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Current large deviation function for the open asymmetric simple exclusion process
• An Exact Formula for the Statistics of the Current in the TASEP with Open Boundaries
• Large deviations and dynamical phase transitions in stochastic chemical networks
• Generic Dynamical Phase Transition in One-Dimensional Bulk-Driven Lattice Gases with Exclusion
• Some Exact Results for the Exclusion Process
• Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton
• Bethe Ansatz and Q-operator for the open ASEP
• Matrix Ansatz for the Fluctuations of the Current in the ASEP with Open Boundaries
• Two-point generating function of the free energy for a directed polymer in a random medium
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states
• Riemann surfaces for KPZ with periodic boundaries
• Large deviations in the symmetric simple exclusion process with slow boundaries
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice - bulk eigenvalues
• Long time asymptotics of the totally asymmetric simple exclusion process
• Current fluctuations and large deviations for periodic TASEP on the relaxation scale
• Rate dependence of current and fluctuations in jump models with negative differential mobility
• Perturbative solution for the spectral gap of the weakly asymmetric exclusion process
• KPZ fluctuations in finite volume
• Integrability of two-species partially asymmetric exclusion processes
• Current fluctuations for totally asymmetric exclusion on the relaxation scale
• $T$-$Q$ relations for the integrable two-species asymmetric simple exclusion process with open boundaries
• Current fluctuations in a partially asymmetric simple exclusion process with a defect particle
• Self-duality and shock dynamics in the $n$-component priority ASEP
• Riemann surfaces for integer counting processes
• From the Riemann surface of TASEP to ASEP
• Mapping current and activity fluctuations in exclusion processes: consequences and open questions