Related papers: Localization and Mobility Edge in One-Dimensional …
Spatial networks are networks where nodes are located in a space equipped with a metric. Typically, the space is two-dimensional and until recently and traditionally, the metric that was usually considered was the Euclidean distance. In…
In a temporal graph, each edge is available at specific points in time. Such an availability point is often represented by a ''temporal edge'' that can be traversed from its tail only at a specific departure time, for arriving in its head…
I discuss the relationship between edge exponents in the statistics of work done, dynamical phase transitions, and the role of different kinds of excitations appearing when a non-equilibrium protocol is performed on a closed, gapped,…
We pinpoint the spectral decomposition for the Anderson tight-binding model with an unbounded random potential on the Bethe lattice of sufficiently large degree. We prove that there exist a finite number of mobility edges separating…
An analytical theory, based on the perturbative treatment of the disorder and extended into a self-consistent set of equations for the dynamical density correlations, is developed and applied to the prototype one-dimensional model of…
We investigate straight-line drawings of topological graphs that consist of a planar graph plus one edge, also called almost-planar graphs. We present a characterization of such graphs that admit a straight-line drawing. The…
The probability distribution of the conductance p(g) of disordered 2d and 3d systems is calculated by transfer matrix techniques. As expected, p(g) is Gaussian for extended states while for localized states it is log-normal. We find that at…
We study the statistical properties of a cellular automata model of traffic flow with the look-ahead potential. The model defines stochastic rules for the movement of cars on a lattice. We analyze the underlying statistical assumptions…
We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…
We study the localization length of a pair of two attractively bound particles moving in a one-dimensional random potential. We show in which way it depends on the interaction potential between the constituents of this composite particle.…
Transport properties of narrow two-dimensional conducting wires in which the electron scattering is caused by side edges' roughness have been studied. The method for calculating dynamic characteristics of such conductors is proposed which…
Based on our recently proposed plane wave framework, we theoretically study the localized-extended transition in the one dimensional incommensurate systems with cosine type of potentials, which are in close connection to many recent…
Some popular mechanisms for restricting the diffusion of waves include introducing disorder (to provoke Anderson localization) and engineering topologically non-trivial phases (to allow for topological edge states to form). However, other…
When nodes in a mobile network cluster together or move according to common external factors (e.g., cars that follow the road network), the resulting contact patterns become correlated. In this work we address the question of modelling such…
The object of study is a soft random geometric graph with vertices given by a Poisson point process on a line and edges between vertices present with probability that has a polynomial decay in the distance between them. Various aspects of…
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,…
It is shown, using high-precision numerical simulations, that the mobility edge of the 3d Anderson model depends on the boundary hopping term t in the infinite size limit. The critical exponent is independent of it. The renormalized…
The presence of frozen uncorrelated random on-site potential in interacting quantum systems can induce a transition from an ergodic phase to a localized one, the so-called many-body localization. Here we numerically study the effects of…
The combined influence of disorder and interactions on the transport properties of electrons in one dimension is investigated. The numerical simulations are carried out by means of the Hartree-Fock-based diagonalization (HFD), a very…
Edge currents of paramagnetic colloidal particles propagate at the edge between two topologically equivalent magnetic lattices of different lattice constant when the system is driven with periodic modulation loops of an external magnetic…