07/02/2024, 16:00 — 17:00 — Online
Gunter Schütz, Forschungszentrum Jülich
Mesoscale mode coupling theory for the weakly asymmetric simple exclusion process
To study fluctuations in the weakly asymmetric simple exclusion process at large space scale $x\varepsilon^{-1}$, large time scale $t \varepsilon^{-\chi}$ and weak hopping bias $b \varepsilon^{\kappa}$ in the limit $\varepsilon \to 0$ we develop a mesoscale mode coupling theory (MMCT) that allows for probing the crossover at $\kappa=1/2$ and $\chi=2$ from Kardar-Parisi-Zhang (KPZ) to Edwards-Wilkinson (EW) universality. The dynamical structure function is shown to satisfy an integral equation that is independent of the microscopic model parameters and has a solution that yields a scale-invariant function with the KPZ dynamical exponent $z=3/2$ at scale $\chi=3/2+\kappa$ for $0\leq\kappa<1/2$ and for $\chi=2$ the exact Gaussian EW solution with $z=2$ for $\kappa>1/2$. At the crossover point it is a function of both scaling variables which converges at macroscopic scale to the conventional mode coupling approximation of KPZ universality for $\kappa<1/2$. This fluctuation pattern confirms long-standing conjectures for $\kappa \leq 1/2$ and is in agreement with mathematically rigorous results for $\kappa>1/2$ despite the numerous uncontrolled approximations on which mode coupling theory is based.
