Related papers: Localization on quantum graphs with random vertex …
We study the region of complete localization in a class of random operators which includes random Schr\"odinger operators with Anderson-type potentials and classical wave operators in random media, as well as the Anderson tight-binding…
We review recent progress in understanding the physical meaning of quantum graph models through analysis of their vertex coupling approximations.
We extend methods of Ding and Smart from their breakthrough paper in 2020 which showed Anderson localization for certain random Schr\"odinger operators on $\ell^2(\mathbb{Z}^2)$ via a quantitative unique continuation principle and Wegner…
We consider quantum graphs with transparent branching points. To design such networks, the concept of transparent boundary conditions is applied to the derivation of the vertex boundary conditions for the linear Schrodinger equation on…
In this note we review some results on localization and related properties for random Schr\"odinger operators arising in aperiodic media. These include the Anderson model associated to disordered quasycrystals and also the so-called Delone…
We consider a class of ensembles of lattice Schr\"odinger operators with deterministic random potentials, including quasi-periodic potentials with Diophantine frequencies, depending upon an infinite number of parameters in an auxiliary…
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
We discuss approximations of vertex couplings of quantum graphs using families of thin branched manifolds. We show that if a Neumann type Laplacian on such manifolds is amended by suitable potentials, the resulting Schr\"odinger operators…
Adapting a definition of Aaronson and Ambainis [Theory Comput. 1 (2005), 47--79], we call a quantum dynamics on a digraph "saturated Z-local" if the nonzero transition amplitudes specifying the unitary evolution are in exact correspondence…
We apply the quotient graph theory described by Band, Berkolaiko, Joyner and Liu to particular graphs symmetric with respect to $S_3$ and $C_3$ symmetry groups. We find the quotient graphs for the three-edge star quantum graph with Neumann…
We prove localization at the bottom of the spectrum for a random Schr\"odinger operator in the continuum with a single-site potential probability distribution supported by a Cantor set of zero Lebesgue measure. This distribution is too…
In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of…
We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an…
Using the concept of intrinsic metric on a locally finite weighted graph, we give sufficient conditions for the magnetic Schr\"odinger operator to be essentially self-adjoint. The present paper is an extension of some recent results proven…
We study localisation effects of strong disorder on the spectral and dynamical properties of (matrix and scalar) Schroedinger operators with non-monotone random potentials, on the d-dimensional lattice. Our results include dynamical…
We consider the quantum graph Hamiltonian on the square lattice in Euclidean space, and we show that the spectrum of the Hamiltonian converges to the corresponding Schr\"odinger operator on the Euclidean space in the continuum limit, and…
We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional…
We discuss various approaches to localization results for one-dimensional random Schr\"odinger operators, both discrete and continuum. We focus in particular on the approach based on F\"urstenberg's Theorem and the Kunz-Souillard method.…
We analyze the singular spectrum of selfadjoint operators which arise from pasting a finite number of boundary relations with a standard interface condition. A model example for this situation is a Schroedinger operator on a star-shaped…
The dimensionality of kernels for Lindbladian superoperators is of physical interest in various scenarios out of equilibrium, for example in mean-field methods for driven-dissipative spin lattice models that give rise to phase diagrams with…