Exact closure and solution for spatial correlations in single-file diffusion

Aurélien Grabsch (1) , Alexis Poncet (1) , Pierre Rizkallah (2) , Pierre Illien (2) , Olivier Bénichou (1)

1 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée
2 PHENIX - PHysicochimie des Electrolytes et Nanosystèmes InterfaciauX

In single-file transport particles diffuse in narrow channels while not overtaking each other. it is a fundamental model for the tracer subdiffusion observed in confined systems, such as zeolites or carbon nanotubes. This anomalous behavior originates from strong bath-tracer correlations in one dimension. Despite extensive effort, these remained elusive, because they involve an infinite hierarchy of equations. For the symmetric exclusion process, a paradigmatic model of single-file diffusion, we break the hierarchy to unveil and solve a closed exact equation satisfied by these correlations. Beyond quantifying the correlations, the role of this key equation as a tool for interacting particle systems is further demonstrated by its application to out-of-equilibrium situations, other observables, and other representative single-file systems.

Domaines: Physique [physics]

Aurélien Grabsch, Alexis Poncet, Pierre Rizkallah, Pierre Illien, Olivier Bénichou. Exact closure and solution for spatial correlations in single-file diffusion. Science Advances , 2022, 8 (12), pp.eabm5043. ⟨10.1126/sciadv.abm5043⟩. ⟨hal-03632097⟩