Related papers: Numerical methods for localization
We propose a realization of the one-dimensional random dimer model and certain N-leg generalizations using cold atoms in an optical lattice. We show that these models exhibit multiple delocalization energies that depend strongly on the…
We study the dynamics of a monitored single particle in a one-dimensional, Anderson-localized system. The time evolution is governed by Hamiltonian dynamics for fixed time intervals, interrupted by local, projective measurements. The…
We use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional, continuum, Anderson-type models with singular distributions; in particular the case of a Bernoulli distribution is covered. The…
Regarding the concepts of urban management, digital transformation, and smart cities, various issues are presented. Currently, we like to attend to location allocation problems that can be a new part of digital transformation in urban…
The localization landscape gives direct access to the localization of bottom-of-band eigenstates in non-interacting disordered systems. We generalize this approach to eigenstates at arbitrary energies in systems with or without internal…
We present a full analytical solution for the localisation length in the one-dimensional Anderson model with weak diagonal disorder in the vicinity of the band centre. The results are obtained with the Hamiltonian map approach that turns…
We study the localization of zeros of Cauchy transforms of discrete measures on the real line. This question is motivated by the theory of canonical systems of differential equations. In particular, we prove that the spaces of Cauchy…
I consider random Schr\"odinger operators with exponentially decaying single site potential, which is allowed to change sign. For this model, I prove Anderson localization both in the sense of exponentially decaying eigenfunctions and…
By employing Random Matrix Theory (RMT) and first-principle calculations, we investigated the behavior of Anderson localization in 1D, 2D and 3D systems characterized by a varying disorder. In particular, we considered random binary layer…
Anderson localisation is an important phenomenon arising in many areas of physics, and here we explore it in the context of quantum information devices. Finite dimensional spin chains have been demonstrated to be important devices for…
We prove Anderson localization for the discrete Laplace operator on radial tree graphs with random branching numbers. Our method relies on the representation of the Laplace operator as the direct sum of half-line Jacobi matrices whose…
We consider the multi-particle Anderson model on the lattice with infinite range but sub-exponentially decaying interaction and show the Anderson localization consisting of the spectral exponential and the strong dynamical localization. In…
Anderson localization of light is traditionally described in analogy to electrons in a random potential. Within this description the disorder strength -- and hence the localization characteristics -- depends strongly on the wavelength of…
The physical position is crucial in location-aware services or protocols based on geographic information, where localization is performed given a set of sensor measurements for acquiring the position of an object with respect to a certain…
It is considered an equation for the Lyapunov exponent $% \gamma $ in a random metric for a scalar propagating wave field. At first order in frequency this equation is solved explicitly. The localization length $L_{c}$ (reciprocal of…
In order to make full use of geographic routing techniques developed for sensor networks, nodes must be localized. However, traditional localization and virtual localization techniques are dependent either on expensive and sometimes…
In electromagnetic source localization problems stemming from linearized Poisson-type equation, the aim is to locate the sources within a domain that produce given measurements on the boundary. In this type of problem, biasing of the…
The elucidation of many physical problems in science and engineering is subject to the accurate numerical modelling of complex wave propagation phenomena. Over the last decades, high-order numerical approximation for partial differential…
We show that, in contrast to immediate intuition, Anderson localization of noninteracting particles induced by a disordered potential in free space can increase (i.e., the localization length can decrease) when the particle energy…
We present a novel approach for relocalization or place recognition, a fundamental problem to be solved in many robotics, automation, and AR applications. Rather than relying on often unstable appearance information, we consider a situation…