Spectral Statistics for Weakly Correlated Random Potentials
نویسنده
چکیده
Abstract. We study localization and derive stochastic estimates (in particular, Wegner and Minami estimates) for the eigenvalues of weakly correlated random discrete Schrödinger operators in the localized phase. We apply these results to obtain spectral statistics for general discrete alloy type models where the single site perturbation is neither of finite rank nor of fixed sign. In particular, for the models under study, the random potential exhibits correlations at any range.
منابع مشابه
Laser probing of random weakly scattering media
An analysis of measurements of phase and amplitude scintillations imparted on a Gaussian laser beam probing a weakly scattering random medium is presented. The second-order statistics (correlation functions and spectral densities) of the detector fluctuations (for homodyne and heterodyne interferometers) are related to the corresponding stochastic properties of the scattering medium. In the pla...
متن کاملRandom coincidence point results for weakly increasing functions in partially ordered metric spaces
The aim of this paper is to establish random coincidence point results for weakly increasing random operators in the setting of ordered metric spaces by using generalized altering distance functions. Our results present random versions and extensions of some well-known results in the current literature.
متن کاملStability of the Absolutely Continuous Spectrum of Random Schrödinger Operators on Tree Graphs
The subject of this work are random Schrödinger operators on regular rooted tree graphs T with stochastically homogeneous disorder. The operators are of the form Hλ(ω) = T + U + λV (ω) acting in l(T), with T the adjacency matrix, U a radially periodic potential, and V (ω) a random potential. This includes the only class of homogeneously random operators for which it was proven that the spectrum...
متن کاملDecorrelation estimates for random discrete schrodinger operators in dimension one and applications to spectral statistics
The purpose of the present work is to establish decorrelation estimates for some random discrete Schrödinger operator in dimension one. We prove that the Minami estimates are consequences of the Wegner estimates and Localization. We also prove decorrelation estimates at distinct energies for the random hopping model and Schrödinger operators with alloy-type potentials. These results are used to...
متن کاملLong-Range Spatial Correlations of Eigenfunctions in Quantum Disordered Systems
This paper is devoted to the statistics of the quantum eigenfunctions in an ensemble of finite disordered systems (metallic grains). We focus on moments of inverse participation ratio. In the universal random matrix limit that corresponds to the infinite conductance of the grains, these moments are self-averaging quantities. At large but finite conductance the moments do fluctuate due to the lo...
متن کامل