Related papers: Higher-order localization landscape theory of Ande…
In this paper we present a modified localization landscape theory to calculate localized/confined electron and hole states and the corresponding energy eigenvalues without solving a (large) eigenvalue problem. We motivate and demonstrate…
We study a particular class of families of multi-dimensional lattice Schr\"o\-dinger operators with deterministic (including quasi-periodic) potentials generated by the "hull" given by an orthogonal series over the Haar wavelet basis on the…
We present here a model of carrier distribution and transport in semiconductor alloys accounting for quantum localization effects in disordered materials. This model is based on the recent development of a mathematical theory of quantum…
We study the localization of wave functions for one-dimensional Schr\"odinger Hamiltonians with random potentials $V(x)$ with short range correlations and large local fluctuations such that $\int\D{x} \smean{V(x)V(0)}=\infty$. A random…
We consider disordered Hamiltonians given by the Laplace operator subject to arbitrary random self-adjoint singular perturbations supported on random discrete subsets of the real line. Under minimal assumptions on the type of disorder, we…
Wave localization occurs in all types of vibrating systems, in acoustics, mechanics, optics, or quantum physics. It arises either in systems of irregular geometry (weak localization) or in disordered systems (Anderson localization). We…
The nearest-neighbour or local mass terms in theory space among quantum fields, with their generic disordered values, are known to lead to the localisation of mass eigenstates, analogous to Anderson localisation in a one-dimensional…
Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary…
We prove the occurrence of Anderson localisation for a system of infinitely many particles interacting with a short range potential, within the ground state Hartree-Fock approximation. We assume that the particles hop on a discrete lattice…
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…
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…
We show how the localization landscape, originally introduced to bound low energy eigenstates of disordered wave media and many-body quantum systems, can form the basis for hardware-efficient quantum algorithms for solving binary…
We present a new mechanism for generating exponential hierarchies in four-dimensional field theories inspired by Anderson localization in one dimension, exploiting an analogy between the localization of electron energy eigenstates along a…
Localization of electronic wave functions in modern two-dimensional (2D) materials such as graphene can impact drastically their transport and magnetic properties. The recent localization landscape (LL) theory has brought many tools and…
For the multi-particle Anderson model with correlated random potential in the continuum, we show under fairly general assumptions on the inter-particle interaction and the random external potential, the Anderson localization which consists…
The one-dimensional propagation of waves in a bichromatic potential may be modeled by the Aubry-Andr\'e Hamiltonian. The latter presents a delocalization-localization transition, which has been observed in recent experiments using ultracold…
We establish strong dynamical localization for a class of multi-particle Anderson models in a Euclidean space with an alloy-type random potential and a sub-exponentially decaying interaction of infinite range. For the first time in the…
These lectures present some basic ideas and techniques in the spectral analysis of lattice Schrodinger operators with disordered potentials. In contrast to the classical Anderson tight binding model, the randomness is also allowed to…
We prove localization and probabilistic bounds on the minimum level spacing for a random block Anderson model without monotonicity. Using a sequence of narrowing energy windows and associated Schur complements, we obtain detailed…
We present a new perturbation theory for quantum mechanical energy eigenstates when the potential equals the sum of two localized, but not necessarily weak potentials $V_{1}(\vec{r})$ and $V_{2}(\vec{r})$, with the distance $L$ between the…