Finite-Time Fluctuations for the Totally Asymmetric Exclusion Process

2015/11/30 by Sylvain Prolhac · 4 citations
Mathematics · Physics and Astronomy · #Ansatz #Asymmetric simple exclusion process #Bethe ansatz #Eigenvalues and eigenvectors #Lattice (music) #Mathematical physics #Mathematics #Non-equilibrium thermodynamics #Physics #Quantum mechanics #Random Matrices and Applications #Scalar (mathematics) #Stationary state #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1103/physrevlett.116.090601

published as Phys. Rev. Lett. 116, 090601 (2016) · 5+3 pages, 5 figures

openalex publication_date 2016/03/04 · arxiv created 2016/03/07 · arxiv updated 2016/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The one-dimensional totally asymmetric simple exclusion process, 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 nonequilibrium steady state, which occurs on the time scale t∼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.

Citations

• Stochastic integrability and the KPZ equation
• Probability distribution of the free energy of a directed polymer in a random medium
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice-first excited states
• Universal Fluctuations of Growing Interfaces: Evidence in Turbulent Liquid Crystals
• Statistical Physics of Vehicular Traffic and Some Related Systems
• Limiting distributions for a polynuclear growth model with external sources

Cited by

• Bethe roots for periodic TASEP and algebraic curve
• Large time cumulants of the KPZ equation on an interval
• Riemann surfaces for KPZ with periodic boundaries
• Fluctuations of TASEP on a ring in relaxation time scale

Related

• Current fluctuations and large deviations for periodic TASEP on the relaxation scale
• Current fluctuations for totally asymmetric exclusion on the relaxation scale
• Fluctuations of TASEP on a ring in relaxation time scale
• Periodic TASEP with general initial conditions
• Steady-State Properties of a Totally Asymmetric Exclusion Process with Periodic Structure