Related papers: Localization for Schr\"odinger operators with Pois…
We consider Schr\"odinger operators in $\ell^2(\Z)$ whose potentials are obtained by randomly concatenating words from an underlying set $\mathcal{W}$ according to some probability measure $\nu$ on $\mathcal{W}$. Our assumptions allow us to…
We show that one-dimensional Schr{\"o}dinger operators whose potentials arise by randomly concatenating words from an underlying set exhibit exponential dynamical localization (EDL) on any compact set which trivially intersects a finite set…
We consider one-dimensional random Schr\"odinger operators with a background potential, arising in the inverse problem of scattering. We study the influence of the background potential on the essential spectrum of the random Schr\"odinger…
We consider continuum one-dimensional Schr\"odinger operators with potentials that are given by a sum of a suitable background potential and an Anderson-type potential whose single-site distribution has a continuous and compactly supported…
We consider discrete one-dimensional Schr\"odinger operators whose potentials are generated by H\"older continuous sampling along the orbits of a uniformly hyperbolic transformation. For any ergodic measure satisfying a suitable bounded…
The two main results of the article are concerned with Anderson Localization for one-dimensional lattice Schroedinger operators with quasi-periodic potentials with d frequencies. First, in the case d = 1 or 2, it is proved that the spectrum…
We consider continuous one-dimensional multifrequency Schr\"odinger operators, with analytic potential, and prove Anderson localization in the regime of positive Lyapunov exponent for almost all phases and almost all Diophantine…
We provide a complete and self-contained proof of spectral and dynamical localization for the one-dimensional Anderson model, starting from the positivity of the Lyapunov exponent provided by F\"urstenberg's theorem. That is, a…
We study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of…
We study multi-frequency quasi-periodic Schr\"odinger operators on $\mathbb{Z}$ in the regime of positive Lyapunov exponent and for general analytic potentials. Combining Bourgain's semi-algebraic elimination of multiple resonances with the…
We study the spectrum of the one-dimensional Schr\"{o}dinger operator $H_0$ with a matrix singular distributional potential $q=Q'$ where $Q\in L^{2}_{\mathrm{loc}}(\mathbb{R},\mathbb{C}^{m})$. We obtain generalizations of Ismagilov's…
We study a class of Schr\"odinger operators on $\Z^2$ with a random potential decaying as $|x|^{-\dex}$, $0<\dex\leq\frac12$, in the limit of small disorder strength $\lambda$. For the critical exponent $\dex=\frac12$, we prove that the…
We study low-energy properties of the random displacement model, a random Schr\"odinger operator describing an electron in a randomly deformed lattice. All periodic displacement configurations which minimize the bottom of the spectrum are…
In this paper, we prove pure point spectrum for a large class of Schr\"odinger operators over circle maps with conditions on the rotation number going beyond the Diophantine. More specifically, we develop the scheme to obtain pure point…
The present paper is devoted to new, improved bounds for the eigenfunctions of random operators in the localized regime. We prove that, in the localized regime with good probability, each eigenfunction is exponentially decaying outside a…
As a supplement of our previous work, we consider the localized region of the random Schroedinger operators on $l^2({\bf Z}^d)$ and study the point process composed of their eigenvalues and corresponding localization centers. For the…
We consider Schr\"odinger operators on periodic discrete graphs. It is known that the spectrum of these operators has band structure. We obtain a localization of spectral bands in terms of eigenvalues of Dirichlet and Neumann operators on a…
We show that the measure of the spectrum of Schr\"odinger operator with potential defined by non-constant function over any minimal aperiodic finite subshift tends to zero, as the coupling constant tends to infinity. We also obtained a…
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 investigate the integrated density of states of the Schr\"odinger operator in the Euclidean plane with a perpendicular constant magnetic field and a random potential. For a Poisson random potential with a non-negative algebraically…