Related papers: One Parameter Scaling Theory for Stationary States…
The Anderson model in one dimension is a quantum particle on a discrete chain of sites with nearest-neighbor hopping and random on-site potentials. It is a progenitor of many further models of disordered systems, and it has spurred numerous…
Stationary probability distributions of one-dimensional random walks on lattices with aperiodic disorder are investigated. The pattern of the distribution is closely related to the diffusional behavior, which depends on the wandering…
The distribution of energy level separations for lattices of sizes up to 28$\times$28$\times$28 sites is numerically calculated for the Anderson model. The results show one-parameter scaling. The size-independent universality of the…
1D diagonally disordered chain with Frenkel exciton and long range exponential intersite interaction is considered. It is shown that some states of this disordered system are delocalised (extended) contrary to the popular statement that all…
Numerical approaches to Anderson localization face the problem of having to treat large localization lengths while being restricted to finite system sizes. We show that by finite-size scaling of the probability distribution of the local…
The effect of an electric field on conduction in a disordered system is an old but largely unsolved problem. Experiments cover an wide variety of systems - amorphous/doped semiconductors, conducting polymers, organic crystals, manganites,…
We investigate two one-dimensional tight-binding models with disorder that have extended states at zero energy. We use exact and partial diagonalisation of the Hamiltonian to obtain the eigenmodes and the associated participation ratios,…
We study the interplay of disorder and interaction effects including bosonic degrees of freedom in the framework of a generic one-dimensional transport model, the Anderson-Edwards model. Using the density-matrix renormalization group…
We resolve the problem of the violation of single parameter scaling at the zero energy of the Anderson tight-binding model with diagonal disorder. It follows from the symmetry properties of the tight-binding Hamiltonian that this spectral…
The single-parameter scaling hypothesis relating the average and variance of the logarithm of the conductance is a pillar of the theory of electronic transport. We use a maximum-entropy ansatz to explore the logarithm of the energy density,…
Dynamical localization phenomena of monochromatically perturbed standard map (SM) and Anderson map (AM), which are both identified with a two-dimensional disordered system under suitable conditions, are investigated by the numerical…
Continuous One-dimensional models supporting extended states are studied. These delocalized statesoccur at well defined values of the energy and are consequences of simple statistical correlation rules. We explicitly study alloys of…
We discuss the conditions under which an anomaly occurs in conductance and localization length of Anderson model on a lattice. Using the ladder hamiltonian and analytical calculation of average conductance we find the set of resonance…
We study scaling laws for singular perturbation problems associated with a class of two-dimensional martensitic phase transformations and deduce a domain dependence of the scaling law in the singular perturbation parameter. In these…
We conduct a numerical investigation into wave propagation and localization in one-dimensional lattices subject to nonlinear disorder, focusing on cases with fixed input conditions. Utilizing a discrete nonlinear Schr\"odinger equation with…
We adapt a simplified version of the Multi-Scale Analysis presented in \cite{C11} to multi-particle tight-binding Anderson models. Combined with a recent eigenvalue concentration bound for multi-particle systems \cite{C10}, the new method…
The performance of a language model has been shown to be effectively modeled as a power-law in its parameter count. Here we study the scaling behaviors of Routing Networks: architectures that conditionally use only a subset of their…
In this paper, we consider the following nonlinear disordered Stark model: $${\bf i}\partial_tu_n+\delta(u_{n+1}+u_{n-1})+nu_n+v_nu_n+\epsilon |u_n|^{2}u_n=0,\quad n\in\mathbb{Z}.$$ By employing the diagonalization of the associated linear…
A new type of delocalization induced by coherent harmonic perturbations in one-dimensional Anderson-localized disordered systems is investigated. With only a few $M$ frequencies a normal diffusion is realized, but the transition to…
The formation of Stationary Localized states due to a nonlinear dimeric impurity embedded in a perfect 1-d chain is studied here using the appropriate Discrete Nonlinear Schr$\ddot{o}$dinger Equation. Furthermore, the nonlinearity has the…