相关论文: (De)Localization in the Prime Schrodinger Operator
We have numerically investigated localization properties in the one-dimensional tight-binding model with chaotic binary on-site energy sequences generated by a modified Bernoulli map with the stationary-nonstationary chaotic transition…
We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an…
We study localization effects of disorder on the spectral and dynamical properties of Schroedinger operators with random potentials. The new results include exponentially decaying bounds on the transition amplitude and related projection…
In this paper the localization properties of the spectral expansions of distributions related to the self adjoint extension of the Schrodinger operator are investigated. Spectral decompositions of the distributions and some classes of…
We prove exponential and dynamical localization for the Schr\"odinger operator with a nonnegative Poisson random potential at the bottom of the spectrum in any dimension. We also conclude that the eigenvalues in that spectral region of…
Most of the investigations to date on tight-binding, quantum percolation models focused on the quantum percolation threshold, i.e., the analogue to the Anderson transition. It appears to occur if roughly 30% of the hopping terms are…
Random operators may acquire extended states formed from a multitude of mutually resonating local quasi-modes. This mechanics is explored here in the context of the random Schr\"odinger operator on the complete graph. The operators exhibits…
We study a random Schroedinger operator, the Laplacian with random Dirac delta potentials on a torus T^d_L = R^d/LZ^d, in the thermodynamic limit L\to\infty, for dimension d=2. The potentials are located on a randomly distorted lattice…
In this article, we study the Schr\"odinger operator for a large class of periodic potentials with the symmetry of a hexagonal tiling of the plane. The potentials we consider are superpositions of localized potential wells, centered on the…
A weakly disordered quasi-one-dimensional tight-binding hopping model with $N$ rows is considered. The probability distribution of the Landauer conductance is calculated exactly in the middle of the band, $\epsilon=0$, and it is shown that…
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…
We study localization properties of electronic states in one-dimensional lattices with nearest-neighbour interaction. Both the site energies and the hopping amplitudes are supposed to be of arbitrary form. A few cases are considered in…
We provide a simple proof of dynamical delocalization, that is, time-increasing lower bounds on quantum transport for discrete, one-particle Schrodinger operators on $\ell^2 (\mathbb{Z}^d)$, provided solutions to the Schrodinger equation…
We study a one-dimensional Anderson model in which one site interacts with a detector monitoring the occupation of that site. We demonstrate that such an interaction, no matter how weak, leads to total delocalization of the Anderson model,…
We study half-line Schr\"odinger operators with locally $H^{-1}$ potentials. In the first part, we focus on a general spectral theoretic framework for such operators, including a Last--Simon-type description of the absolutely continuous…
We investigate the localization properties of a one-dimensional bichromatic optical lattice in the tight binding regime, by discussing how exponentially localized states emerge upon changing the degree of commensurability. We also review…
Results of large-scale numerical simulations are reported on the Anderson localization in a two-dimensional square lattice tight-binding model with random flux. Localization lengths, fluctuations of the conductance, and the density of…
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…
The perturbation theory is developed for joint statistics of the advanced and retarded Green's functions of the 1D Schrodinger equation with a piecewise-constant random potential. Using this method, analytical expressions are obtained for…
Let $\mathcal{L}$ be a fixed $d$-dimensional lattice. We study the localization properties of solutions of the stationary Schr\"odinger equation with a positive $L^\infty$ potential on tori $\mathbb{R}^d/L\mathcal{L}$ in the limit, as…