Generalized Correlation Profiles in Single-File Systems

Single-file diffusion refers to the motion in narrow channels of particles which cannot bypass each other, and leads to tracer subdiffusion. Most approaches to this celebrated many-body problem were restricted to the description of the tracer only. Here, we go beyond this standard description by introducing and providing analytical results for generalized correlation profiles (GCPs) in the frame of the tracer. In addition to controlling the statistical properties of the tracer, these quantities fully characterize the correlations between the tracer position and the bath particles density. Considering the hydrodynamic limit of the problem, we determine the scaling form of the GCPs with space and time, and unveil a nonmonotonic dependence with the distance to the tracer despite the absence of any asymmetry. Our analytical approach provides several exact results for the GCPs for paradigmatic models of single-file diffusion, such as Brownian particles with hardcore repulsion, the symmetric exclusion process and the random average process. The range of applicability of our approach is further illustrated by considering (i) extensions to general interactions between particles, (ii) the out-of-equilibrium situation of an initial step of density, and (iii) beyond the hydrodynamic limit, the GCPs at arbitrary time in the dense limit.

Automated summary

Single-file diffusion involves particles moving in narrow channels without being able to bypass each other, leading to tracer subdiffusion. The study introduces and provides analytical results for generalized correlation profiles (GCPs) within the frame of the tracer, fully characterizing correlations between the tracer position and bath particles density. The analytical approach offers exact results for GCPs in paradigmatic models of single-file diffusion, highlighting the nonmonotonic dependence with distance to the tracer despite symmetry.