Cumulant generating functions of a tracer in quenched dense symmetric exclusion processes

Abstract

The Symmetric Exclusion Process (SEP), where particles hop on a 1D lattice with the restriction that there can only be one particle per site, is a paradigmatic model of interacting particle systems. Recently, it has been shown that the nature of the initial conditions - annealed or quenched - has a quantitative impact on the long-time properties of tracer diffusion. However, so far, all the studies in the quenched case focused on the low-density limit of the SEP. Here, we derive the cumulant generating function of the tracer position in the dense limit with quenched initial conditions. Importantly, our approach also allows us to consider the nonequilibrium situations of (i) a biased tracer in the SEP and (ii) a symmetric tracer in a step of density. In the former situation, we show that the initial conditions have a striking impact, and change the very dependence of the cumulants on the bias.

References in corpus (17)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Persistence exponents for fluctuating interfaces
• From random walk to single-file diffusion
• Large Deviations in Single File Diffusion
• 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
• The Exclusion Process: A paradigm for non-equilibrium behaviour
• The Lasting Effect of Initial Conditions on Single File Diffusion
• Motion of a driven tracer particle in a one-dimensional symmetric lattice gas
• Langevin formulation for single-file diffusion
• Universal Large Deviations for the Tagged Particle in Single File Motion
• Large deviations of a tracer in the symmetric exclusion process
• Large deviation function of a tracer position in single file diffusion
• Dynamical properties of single-file diffusion
• Correlation and fluctuation in Random Average Process on an infinite line with a driven tracer
• Bath-Mediated Interactions between Driven Tracers in Dense Single-Files
• Driven Tracers in a One-Dimensional Periodic Hard-Core Lattice Gas

Cited by in corpus (8)

• Exact solution of the macroscopic fluctuation theory for the symmetric exclusion process
• Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model
• Role of initial conditions in $1D$ diffusive systems: compressibility, hyperuniformity and long-term memory
• Macroscopic fluctuations of a driven tracer in the symmetric exclusion process
• From Particle Currents to Tracer Diffusion: Universal Correlation Profiles in Single-File Dynamics
• Driven Tracer in the Symmetric Exclusion Process: Linear Response and Beyond
• Large deviations of a tracer position in the dense and the dilute limits of a single-file diffusion
• Exact time dependence of the cumulants of a tracer position in a dense lattice gas