Finite-time fluctuations for the totally asymmetric exclusion process

Abstract

The one-dimensional totally asymmetric simple exclusion process (TASEP), a Markov process describing classical hard-core particles hopping in the same direction, is considered on a periodic lattice of $L$ sites. The relaxation to the non-equilibrium steady state, which occurs on the time scale $t\sim L^{3/2}$ for large $L$, is studied for the half-filled system with $N=L/2$ particles. Using large $L$ asymptotics of Bethe ansatz formulas for the eigenstates, exact expressions depending explicitly on the rescaled time $t/L^{3/2}$ are obtained for the average and two-point function of the local density, and for the current fluctuations for simple (stationary, flat and step) initial conditions, relating previous results for the infinite system to stationary large deviations. The final formulas have a nice interpretation in terms of a functional integral with the action of a scalar field in a linear potential.

5+3 pages, 5 figures

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Cited by in corpus (30)

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• Systematic time expansion for the Kardar-Parisi-Zhang equation, linear statistics of the GUE at the edge and trapped fermions
• Kardar-Parisi-Zhang Universality of the Nagel-Schreckenberg Model
• TASEP on a ring in sub-relaxation time scale
• Topology and the Kardar-Parisi-Zhang universality class
• Tail of the two-time height distribution for KPZ growth in one dimension
• Delta-Bose gas on a half-line and the KPZ equation: boundary bound states and unbinding transitions
• Riemann surfaces for KPZ with periodic boundaries
• Direct Evidence for Universal Statistics of Stationary Kardar-Parisi-Zhang Interfaces
• Multi-point distribution of periodic TASEP
• Integral formulas of ASEP and $q$-TAZRP on a ring
• Extrapolation methods and Bethe ansatz for the asymmetric exclusion process
• Brownian bridges for late time asymptotics of KPZ fluctuations in finite volume
• Riemann surface for TASEP with periodic boundaries
• Perturbative solution for the spectral gap of the weakly asymmetric exclusion process
• Finite-size and finite-time effects in large deviation functions near dynamical symmetry breaking transitions
• KPZ fluctuations in finite volume
• Periodic TASEP with general initial conditions
• Riemann surfaces for integer counting processes
• Current statistics in the q-boson zero range process
• From the Riemann surface of TASEP to ASEP
• Height fluctuations of stationary TASEP on a ring in relaxation time scale
• Approach to stationarity for the KPZ fixed point with boundaries
• Fluctuations of TASEP on a ring in relaxation time scale
• Lifted TASEP: long-time dynamics,generalizations, and continuum limit
• Current fluctuations for the second class particle : joint statistics
• Nonequilibrium phases and quantum correlations in synthetic transport models
• Multi-point distribution of discrete time periodic TASEP
• Mapping current and activity fluctuations in exclusion processes: consequences and open questions