Directed polymer in random media with a defect

Jamming and condensation in one-dimensional driven flow

We revisit the slow-bond (SB) problem of the one-dimensional (1D) totally asymmetric simple exclusion process (TASEP) with modified hopping rates. In the original SB problem, it turns out that a local defect is always relevant to the system as jamming, so that phase separation occurs in the 1D TASEP. However, crossover scaling behaviors are also observed as finite-size effects. In order to check if the SB can be irrelevant to the system with particle interaction, we employ the condensation concept in the zero-range process. The hopping rate in the modified TASEP depends on the interaction parameter and the distance up to the nearest particle in the moving direction, besides the SB factor. In particular, we focus on the interplay of jamming and condensation in the current-density relation of 1D driven flow. Based on mean-field calculations, we present the fundamental diagram and the phase diagram of the modified SB problem, which are numerically checked. Finally, we discuss how the condensation of holes suppresses the jamming of particles and vice versa, where the partially condensed phase is the most interesting, compared to that in the original SB problem.

Effects of a local defect on one-dimensional nonlinear surface growth

The slow-bond problem is a long-standing question about the minimal strength ε_{c} of a local defect with global effects on the Kardar-Parisi-Zhang (KPZ) universality class. A consensus on the issue has been delayed due to the discrepancy between various analytical predictions claiming ε_{c}=0 and numerical observations claiming ε_{c}>0. We revisit the problem via finite-size scaling analyses of the slow-bond effects, which are tested for different boundary conditions through extensive Monte Carlo simulations. Our results provide evidence that the previously reported nonzero ε_{c} is an artifact of a crossover phenomenon which logarithmically converges to zero as the system size goes to infinity.

Effects of junctional correlations in the totally asymmetric simple exclusion process on random regular networks

We investigate the totally asymmetric simple exclusion process on closed and directed random regular networks, which is a simple model of active transport in the one-dimensional segments coupled by junctions. By a pair mean-field theory and detailed numerical analyses, it is found that the correlations at junctions induce two notable deviations from the simple mean-field theory, which neglects these correlations: (1) the narrower range of particle density for phase coexistence and (2) the algebraic decay of density profile with exponent 1/2 even outside the maximal-current phase. We show that these anomalies are attributable to the effective slow bonds formed by the network junctions.