Passive Tracer Dynamics in Slow-Bond Problem

Asymptotic Kardar-Parisi-Zhang (KPZ) properties are investigated in the totally asymmetric simple exclusion process (TASEP) with a localized geometric defect. In particular, we focus on the universal nature of nonequilibrium steady states of the modified TASEP. Since the original TASEP belongs to the KPZ universality class, it is mathematically and physically a quite interesting question whether the localized columnar defect, the slow bond (SB), is really always relevant to the KPZ universality or not. However, it is numerically controversial to address the possibility of the non-queued SB phase in the weak-strength SB limit. Based on the detailed statistical analysis of KPZ-type growing interfaces, we present a comprehensive view of the non-queue SB phase, compared to finite-size crossover effects that reported in our earlier work [Soh {\it et al.}, Phys. Rev. E {\bf 95}, 042123 (2017)]. Moreover, we employ two types of passive tracer dynamics as the probe of the SB dynamics. Finally, we provide intuitive arguments for additional clues to resolve the controversy of the SB problem.