Related papers: Localization and Mobility Edge in One-Dimensional …
A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…
Locally periodic rods, which show approximate invariance with respect to translations, are constructed by joining $N$ unit cells. The spectrum then shows a band spectrum. We then break the local periodicity by including one or more defects…
A graph drawn in the plane with straight-line edges is called a geometric graph. If no path of length at most $k$ in a geometric graph $G$ is self-intersecting we call $G$ $k$-locally plane. The main result of this paper is a construction…
We consider the problem of using location queries to monitor the congestion potential among a collection of entities moving, with bounded speed but otherwise unpredictably, in $d$-dimensional Euclidean space. Uncertainty in entity locations…
We show, using quasi-exact numerical simulations, that Anderson localization of one-dimensional particles in a disordered potential survives in the presence of attractive interaction between particles. The localization length of the…
Localization is a fundamental task for sensor networks. Traditional network construction approaches allow to obtain localized networks requiring the nodes to be at least tri-connected (in 2D), i.e., the communication graph needs to be…
We consider two models for a pair of interacting particles in a random potential: (i) two particles with a Hubbard interaction in arbitrary dimensions and (ii) a strongly bound pair in one dimension. Establishing suitable correpondences we…
In this paper, we present a general framework for constructively proving the existence and of stationary localized solutions, spatially periodic solutions, and branches of spatially periodic solutions in the 1D Thomas model. Specifically,…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
We investigate disorder induced localization in the presence of nonlinearity and curvature. We numerically analyze the time-resolved three-dimensional expansion of a wave-packet in a bended cigar shaped potential with a focusing Kerr-like…
In spatial networks vertices are arranged in some space and edges may cross. When arranging vertices in a 1-dimensional lattice edges may cross when drawn above the vertex sequence as it happens in linguistic and biological networks. Here…
Mobility edges (ME), defined as critical energies that separate the extended states from the localized states, are a significant topic in quantum physics. In this paper, we demonstrate the existence of two exact new mobility edges for two…
We propose a method to address the existence of topological edge modes in one-dimensional (1D) nonlinearlattices, by deforming the edge modes of linearized models into solutions of the fully nonlinear system. Forlarge enough nonlinearites,…
We review the research literature investigating systems in which mobile entities can carry data while they move. These entities can be either mobile by nature (e.g., human beings and animals) or mobile by design (e.g., trains, airplanes,…
The mobility edge (ME) is a crucial concept in understanding localization physics, marking the critical transition between extended and localized states in the energy spectrum. Anderson localization scaling theory predicts the absence of ME…
We study localization properties of the eigenstates and wave transport in one-dimensional system consisting of a set of barriers/wells of fixed thickness and random heights. The inherent peculiarity of the system resulting in the enhanced…
We consider a random growth model based on the IDLA protocol with sources in a hyperplane of $Z^d$ . We provide a stabilization result and a shape theorem generalizing [7] in any dimension by introducing new techniques leading to a rough…
We study the localization properties of a test dipole feeling the disordered potential induced by dipolar impurities trapped at random positions in an optical lattice. This random potential is marked by correlations which are a convolution…
The wide spread use of positioning and photographing devices gives rise to a deluge of traffic trajectory data (e.g., vehicle passage records and taxi trajectory data), with each record having at least three attributes: object ID, location…
Extremal graph theory studies the maximum or minimum number of subgraphs isomorphic to a prescribed graph under given constraints. \textit{Localization} has recently emerged as a framework that refines such problems by assigning extremal…