Related papers: Directed Polymers in Random Environment are Diffus…
This lecture is a tutorial introduction to coherent effects in disordered electronic systems. Avoiding technicalities as most as possible, I present some personal points of view to describe well-known signatures of phase coherence like weak…
This review is devoted to the detailed consideration of the universal statistical properties of one-dimensional directed polymers in a random potential. In terms of the replica Bethe ansatz technique we derive several exact results for…
We study the dynamics of a polymer or a D-dimensional elastic manifold diffusing and convected in a non-potential static random flow (the ``randomly driven polymer model''). We find that short-range (SR) disorder is relevant for d < 4 for…
In this article we study a \emph{non-directed} polymer model in dimension $d\ge 2$: we consider a simple symmetric random walk on $\mathbb{Z}^d$ which interacts with a random environment, represented by i.i.d. random variables…
We have obtained the universal conductance distribution of two-dimensional disordered systems in the strongly localized limit. This distribution is directly related to the Tracy-Widom distribution, which has recently appeared in many…
Directed polymers on 1+1 dimensional lattices coupled to a heat bath at temperature $T$ are studied numerically for three ensembles of the site disorder. In particular correlations of the disorder as well as fractal patterning are…
We use numerical simulations to examine two-dimensional particle mixtures that strongly phase separate in equilibrium. When the system is externally driven in the presence of quenched disorder, plastic flow occurs in the form of meandering…
In this note we establish several inequalities and monotonicity properties for the free energy of directed polymers under certain stochastic orders: the usual stochastic order, the Laplace transform order and the convex order. For the…
The universality of the directed polymer model and the analogous KPZ equation is supported by numerical simulations using non-Gaussian random probability distributions in two, three and four dimensions. It is shown that although in the…
We study discrete linear divergence-form operators with random coefficients, also known as the random conductance model. We assume that the conductances are bounded, independent and stationary; the law of a conductance may depend on the…
Localization driven by disorder has a strong influence on the conducting property of conducting polymer. A class of authors hold the opinion that disorder in the material is homogeneous and conducting polymer is disordered metal close to…
The impact of quenched disorder on deterministic diffusion in chaotic dynamical systems is studied. As a simple example, we consider piecewise linear maps on the line. In computer simulations we find a complicated scenario of multiple…
A fundamental insight in the theory of diffusive random walks is that the mean length of trajectories traversing a finite open system is independent of the details of the diffusion process. Instead, the mean trajectory length depends only…
We consider a model of directed polymers on a regular tree with a disorder given by independent, identically distributed weights attached to the vertices. For suitable weight distributions this model undergoes a phase transition with…
We consider a directed variant of the negative-weight percolation model in a two-dimensional, periodic, square lattice. The problem exhibits edge weights which are taken from a distribution that allows for both positive and negative values.…
We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The…
We prove a central limit theorem for the winding number of a directed polymer on a cylinder, which is equivalent with proving the Gaussian fluctuations of the endpoint of the directed polymer in a spatial periodic environment.
We construct and study a family random continuum polymer measures $\mathbf{M}_{r}$ corresponding to limiting partition function laws recently derived in a weak-coupling regime of polymer models on hierarchical graphs with marginally…
We present a unified scaling theory for the structural behavior of polymers embedded in a disordered energy substrate. An optimal polymer configuration is defined as the polymer configuration that minimizes the sum of interacting energies…
Sub-dimensional localization, also known as directional localization, arises when 2d electrons are subject to a periodic potential and incommensurate magnetic field which cause them to become exponentially localized along one crystal axis,…