Related papers: Optimally localized Wannier functions for quasi on…
This paper extends Yosida's mean ergodic theorem in order to compute projections onto non-unitary eigenspaces for spectral operators of scalar-type on locally convex linear topological spaces. For spectral operators with dominating point…
We consider perturbations of quasi-periodic Schr\"odinger operators on the integer lattice with analytic sampling functions by decaying potentials and seek decay conditions under which various spectral properties are preserved. In the…
We consider decaying oscillatory perturbations of periodic Schr\"odinger operators on the half line. More precisely, the perturbations we study satisfy a generalized bounded variation condition at infinity and an $L^p$ decay condition. We…
In this paper we address the problem of estimating the operator norm of the embeddings between multidimensional weighted Paley-Wiener spaces. These can be equivalently thought as Fourier uncertainty principles for bandlimited functions. By…
Wigner phase space quasi-probability distribution function is a Fourier transform related to a given quantum mechanical wave function. It is shown that for the wave functions of type $\psi (q)=e^{-aq^2}\phi (q)$, the Wigner function can be…
Being Wannierizable is not the end of the story for topological insulators. We introduce a family of topological insulators that would be considered trivial in the paradigm set by the tenfold way, topological quantum chemistry, and the…
The spectral landscape and the transport property of a translationally invariant network with side-coupled quantum dots are demonstrated within the tight-binding framework. For periodic environment band structure is demonstrated…
We determine exact exponential asymptotics of eigenfunctions and of corresponding transfer matrices of the almost Mathieu operators for all frequencies in the localization regime. This uncovers a universal structure in their behavior,…
We prove that the random Schrodinger operators on $\mathbb{R}^3$ with independent, identically distributed random variables and single-site potentials given by $\delta$-functions on $\mathbb{Z}^3$, exhibit both dynamical localization and…
We study the discreteness of the spectrum of Schrodinger operators which are defined on N-dimensional rooted trees of a finite or infinite volume, and are subject to a certain mixed boundary condition. We present a method to estimate their…
We derive a multi-band formulation of the orbital magnetization in a normal periodic insulator (i.e., one in which the Chern invariant, or in 2d the Chern number, vanishes). Following the approach used recently to develop the single-band…
Wannier functions of the one dimensional Schroedinger equation with elliptic one gap potentials are explicitly constructed. Properties of these functions are analytically and numerically investigated. In particular we derive an expression…
We construct self-similar functions and linear operators to deduce a self-similar variant of the Laplacian operator and of the D'Alembertian wave operator. The exigence of self-similarity as a symmetry property requires the introduction of…
Topologically protected waves in the linearly polarized Maxwell's equations with gyrotropic, magneto-optic media were studied a decade ago both computationally and experimentally. This paper develops a robust tight-binding model for this…
This paper is devoted to providing quantitative bounds on the location of eigenvalues, both discrete and embedded, of non self-adjoint Lam\'e operators of elasticity $-\Delta^\ast + V$ in terms of suitable norms of the potential $V$. In…
We have constructed maximally-localized Wannier functions for prototype structures of solid molecular hydrogen under pressure, starting from LDA and tight-binding Bloch wave functions. Each occupied Wannier function can be associated with…
For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly-decaying linear potential bearing a localized eigenmode embedded in the continuous spectrum. Here, we extend this idea in two directions:…
The absolutely continuous spectrum of one-dimensional Schr\"odinger operators is proved to be stable under perturbation by potentials satisfying mild decay conditions. In particular, the absolutely continuous spectrum of free and periodic…
Photonic bandgap engineering using aperiodic lattices (ALs) is systematically studied. Up to now ALs have tended to be defined by specific formulae (e.g. Fibonacci, Cantor), and theories have neglected other useful ALs along with the vast…
We prove a quantum ergodicity theorem for sequences of closed hyperbolic surfaces converging to the Poincar\'e disc in the Benjamini-Schramm sense. Assuming a uniform lower bound on the injectivity radius and a spectral gap, we establish…