Related papers: Sharp arithmetic localization for quasiperiodic op…
We prove Anderson localization at the internal band-edges for periodic magnetic Schr{\"o}dinger operators perturbed by random vector potentials of Anderson-type. This is achieved by combining new results on the Lifshitz tails behavior of…
Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-including differential operators-are discontinuous or set-valued,…
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…
In this paper, we present an approach for explicitly constructing quasi-periodic Schr\"odinger operators with Cantor spectrum with $C^k$ potential. Additionally, we provide polynomial asymptotics on the size of spectral gaps.
We consider Schr\"odinger operators with periodic potentials on periodic discrete graphs. Their spectrum consists of a finite number of bands. We obtain two-sided estimates of the total bandwidth for the Schr\"odinger operators in terms of…
In the present paper, we establish a reduction theorem for linear Schr\"odinger equation with finite smooth and time-quasi-periodic potential subject to Dirichlet boundary condition by means of KAM technique. Moreover, it is proved that the…
In this paper we obtain asymptotic formulas of arbitrary order for the Bloch eigenvalue and the Bloch function of the periodic Schrodinger operator of arbitrary dimension, when corresponding quasimomentum lies near a diffraction hyperplane.…
We prove that the wave operators for Schr\"odinger operators with multi-center local point interactions are the scaling limits of the ones for Schr\"odinger operators with regular potentials. We simultaneously present a proof of the…
We consider the Schr\"odinger operator in ${\mathbb R}^n$, $n\geq 3$, with the electric potential $V$ and the magnetic potential $A$ being periodic functions (with a common period lattice) and prove absolute continuity of the spectrum of…
We focus on the linear convergence of generalized proximal point algorithms for solving monotone inclusion problems. Under the assumption that the associated monotone operator is metrically subregular or that the inverse of the monotone…
Averaging certain class of quasiperiodic monotone operators can be simplified to the periodic homogenization setting by mapping the original quasiperiodic structure onto a periodic structure in a higher dimensional space using cut-and…
We show that for almost every frequency alpha \in \R \setminus \Q, for every C^omega potential v:\R/\Z \to R, and for almost every energy E the corresponding quasiperiodic Schrodinger cocycle is either reducible or nonuniformly hyperbolic.…
With derive sharp spectral asymptotics (with the remainder estimate $O(\mu ^{-1}h^{1-d}+\mu ^{\frac{d} {2}-1}h^{1-\frac{d}{2}})$ for $d$-dimensional Schr\"odinger operator with a strong magnetic field; here $h$ and $\mu$ are Plank and…
We prove the existence of ballistic transport for a Schr\"odinger operator with a generic quasi-periodic potential in any dimension $d>1$.
For one-dimensional Schroedinger operators with complex-valued potentials, we construct pseudomodes corresponding to large pseudoeigenvalues. Our (non-semi-classical) approach results in substantial progress in achieving optimal conditions…
We study arbitrary order symmetry operators for the linear Schr\"odinger equations with arbitrary number of spatial variables. We deduce determining equations for coefficient functions of such operators and consider in detail some cases…
We study lower bounds on the Lyapunov exponent associated with one-frequency quasiperiodic Schr\"odinger operators with an added finite valued background potential. We prove that, for sufficiently large coupling constant, the Lyapunov…
In this paper we prove global existence and uniqueness of solutions to the stochastic logarithmic Schr\"odinger equation with linear multiplicative noise. Our approach is mainly based on the rescaling approach and the method of maximal…
We show the sharp global well posedness for the Cauchy problem for the cubic (quartic) non-elliptic derivative Schr\"odinger equations with small rough data in modulation spaces $M^s_{2,1}(\mathbb{R}^n)$ for $n\ge 3$ ($n= 2$). In 2D cubic…
In this article, we establish the arithmetic purity of strong approximation for smooth loci of weighted projective spaces. By using this result and the descent method, we also prove that the arithmetic purity of strong approximation with…