Related papers: Anderson Localization for radial tree-like random …
In 1990, Klein, Lacroix, and Speis proved (spectral) Anderson localisation for the Anderson model on the strip of width $W \geqslant 1$, allowing for singular distribution of the potential. Their proof employs multi-scale analysis, in…
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…
We introduce a class of models containing robust and analytically demonstrable multifractality induced by disorder correlations. Specifically, we investigate the statistics of eigenstates of disordered tight-binding models on two classes of…
This Master's thesis examines the properties of large degree vertices in random recursive directed acyclic graphs (RRDAGs), a generalization of the well-studied random recursive tree (RRT) model. Using a novel adaptation of Kingman's…
We consider the Anderson model at large disorder on $\mathbb{Z}^2$ where the potential has a symmetric Bernoulli distribution. We prove that Anderson localization happens outside a small neighborhood of finitely many energies. These…
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…
Anderson localization has been observed for a variety of media, including ultracold atomic gases with speckle disorder in one and three dimensions. However, observation of Anderson localization in a two-dimensional geometry for ultracold…
We study the multi-particle Anderson model in the continuum and show that under some mild assumptions on the random external potential and the inter-particle interaction, for any finite number of particles, the multi-particle lower edges of…
A technically convenient signature of Anderson localization is exponential decay of the fractional moments of the Green function within appropriate energy ranges. We consider a random Hamiltonian on a lattice whose randomness is generated…
We report on recent results on the spectral statistics of the discrete Anderson model in the localized phase. Our results show, in particular, that, for the discrete Anderson Hamiltonian with smoothly distributed random potential at…
We study a random recursive tree model featuring complete redirection called the random friend tree and introduced by Saram\"aki and Kaski. Vertices are attached in a sequential manner one by one by selecting an existing target vertex and…
Recently, random graphs in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices have attracted much attention. Here, we present a specific realization of a class of random…
We present a study of the transport properties of a general class of quantum mechanical waveguides: Quantum Railroads (QRR). These waveguides are characterised by having a different number of adiabatic modes which carry current in one…
Consider the normalized adjacency matrices of random $d$-regular graphs on $N$ vertices with fixed degree $d\geq3$. We prove that, with probability $1-N^{-1+{\varepsilon}}$ for any ${\varepsilon} >0$, the following two properties hold as $N…
A statistical analysis of the ionization yield of one-dimensional, periodically driven hydrogen Rydberg states is provided. We find excellent agreement with predictions for the conductance across an Anderson-localized, quasi…
A self-consistent theory of the frequency dependent diffusion coefficient for the Anderson localization problem is presented within the tight-binding model of non-interacting electrons on a lattice with randomly distributed on-site energy…
The spatial extension and complexity of the eigenfunctions of an open finite-size two-dimensional (2D) random system are systematically studied for a random collection of systems ranging from weakly scattering to localized. The…
We consider the spectral and dynamical properties of one-dimensional quantum walks placed into homogenous electric fields according to a discrete version of the minimal coupling principle. We show that for all irrational fields the…
In this work we analytically explain the origin of the mobility edge in the partially disordered random regular graphs of degree d, i.e., with a fraction $\beta$ of the sites being disordered, while the rest remain clean. It is shown that…
First we report that the adjacency matrices of real-world complex networks systematically have null eigenspaces with much higher dimensions than that of random networks. These null eigenvalues are caused by duplication mechanisms leading to…