Related papers: Decorrelation estimates for a 1D tight binding mod…
The purpose of the present work is to establish decorrelation estimates for the locally renormalized eigenvalues of the discrete Anderson model near two distinct energies inside the localization region. In dimension one, we prove these…
A simple tight-binding model is used to illustrate how the time dependence of a state vector can be obtained from all the eigenvalues and eigenvectors of the Hamiltonian. The behavior of the eigenvalues and eigenvectors is studied for…
A new reference state for density functional theory, termed the independent atom ansatz, is introduced in this work. This ansatz allows for the exact representation of electron density in terms of non-interacting, atom-localized orbitals.…
The nature of delocalization in a 1D system ruled by a tight-binding Hamiltonian is investigated. Using a local evaluation of the ground state energy, it is shown that the range of the delocalization effects is rather limited. The method is…
This work investigates the implications of relaxing the measurement independence assumption in Bell's theorem by introducing a new class of local deterministic models that account for both particle preparation and measurement settings. Our…
We perform both analytical and numerical studies of the one-dimensional tight-binding Hamiltonian with stochastic uncorrelated on-site energies and non-fluctuating long-range hopping integrals . It was argued recently [A. Rodriguez at al.,…
In the present work, we investigated the correlation-induced localization-delocalization transition in the one-dimensional tight-binding model with fractal disorder. We obtained a phase transition diagram from localized to extended states…
We prove localization and probabilistic bounds on the minimum level spacing for the Anderson tight-binding model on the lattice in any dimension, with single-site potential having a discrete distribution taking N values, with N large.
We consider a fully-discrete approximations of 1-D heat equation with dynamic boundary conditions for which we provide a controllability result. The proof of this result is based on a relaxed observability inequality for the corresponding…
We prove decorrelation estimates for generalized lattice Anderson models on $Z^d$ constructed with finite-rank perturbations in the spirit of Klopp \cite{klopp}. These are applied to prove that the local eigenvalue statistics…
We study overlap of two different eigenfunctions as compared with self-overlap in the framework of an infinite-dimensional version of the disordered tight-binding model. Despite a very sparse structure of the eigenstates in the vicinity of…
A key starting assumption in many classical interatomic potential models for materials is a site energy decomposition of the potential energy surface into contributions that only depend on a small neighbourhood. Under a natural stability…
Domain specific localization of eigenstates has been a persistent observation for systems with local symmetries. The underlying mechanism for this localization behaviour has however remained elusive. We provide here an analysis of locally…
We report a calculation of the correlation function of the local density of states in a disordered quasi-one-dimensional wire in the unitary symmetry class at a small energy difference. Using an expression from the supersymmetric…
We prove decorrelation estimates for generalized lattice Anderson models on $Z^d$ constructed with finite-rank perturbations in the spirit of Klopp \cite{klopp}. These are applied to prove that the local eigenvalue statistics…
Given a bipartite system, correlations between its subsystems can be understood as information that each one carries about the other. In order to give a model-independent description of secure information disposal, we propose the paradigm…
In an entanglement swapping process two initially uncorrelated qubits become entangled, without any direct interaction. We present a model using local variables aiming at reproducing this remarkable process, under the realistic assumption…
The purpose of the present work is to establish decorrelation estimates at distinct energies for some random Schr{\"o}dinger operator in dimension one. In particular, we establish the result for some random operators on the continuum with…
In this paper we study the local spectral statistics in the localised region of various random operator models, including the $d$-dimensional the Anderson model and random Schr\"odinger operators. It is already established, in the above…
We consider gapless models of statistical mechanics. At zero temperatures correlation functions decay asymptotically as powers of distance in these models. Temperature correlations decay exponentially. We used an example of solvable model…