Competing effects of point versus columnar defects on the roughening of directed polymers in random media

Nonequilibrium processes: driven lattice gases, interface dynamics, and quenched-disorder effects on density profiles and currents

Properties of the one-dimensional totally asymmetric simple exclusion process (TASEP), and their connection with the dynamical scaling of moving interfaces described by a Kardar-Parisi-Zhang equation are investigated. With periodic boundary conditions, scaling of interface widths (the latter defined via a discrete occupation-number-to-height mapping), gives the exponents alpha=0.500(5) , z=1.52(3) , beta=0.33(1) . With open boundaries, results are as follows: (i) in the maximal-current phase, the exponents are the same as for the periodic case, and in agreement with recent Bethe ansatz results; (ii) in the low-density phase, curve collapse can be found to a rather good extent, with alpha=0.497(3) , z=1.20(5) , beta=0.41(2) , which is apparently at variance with the Bethe ansatz prediction z=0 ; (iii) on the coexistence line between low- and high-density phases, alpha=0.99(1) , z=2.10(5) , beta=0.47(2) , in relatively good agreement with the Bethe ansatz prediction z=2 . From a mean-field continuum formulation, a characteristic relaxation time, related to kinematic-wave propagation and having an effective exponent z;{'}=1 , is shown to be the limiting slow process for the low-density phase, which accounts for the above mentioned discrepancy with Bethe ansatz results. For TASEP with quenched bond disorder, interface width scaling gives alpha=1.05(5) , z=1.7(1) , beta=0.62(7) . From a direct analytic approach to steady-state properties of TASEP with quenched disorder, closed-form expressions for the piecewise shape of averaged density profiles are given, as well as rather restrictive bounds on currents. All these are substantiated in numerical simulations.

Localization in disordered media, anomalous roughening, and coarsening dynamics of faceted surfaces

We study a surface growth model related to the Kardar-Parisi-Zhang equation for nonequilibrium kinetic roughening, but where the thermal noise is replaced by a static columnar disorder eta(x) . This model is one of the many representations of the problem of particle diffusion in trapping or amplifying disordered media. We find that probability localization in the latter translates into facet formation in the equivalent surface growth problem. Coarsening of the pattern can therefore be identified with the diffusion of the localization center. The emergent faceted structure gives rise to nontrivial scaling properties, including anomalous surface roughening in excellent agreement with an existing conjecture for kinetic roughening of faceted surfaces. In a wider context, our study sheds light onto the scaling properties in other systems displaying this kind of patterned surface.

Scaling of polymers in aligned rods

We study the behavior of self-avoiding polymers in a background of infinitely long vertically aligned rods that are either frozen in random positions or free to move horizontally. We find that in both cases the polymer chains are highly elongated, with vertical and horizontal size exponents that differ by a factor of 3. Though these results are different than previous predictions, our results are confirmed by detailed computer simulations.