Spectral Statistics for the Discrete Anderson Model in the Localized Regime
نویسنده
چکیده
We report on recent results on the spectral statistics of the discrete Anderson model in the localized phase obtained in [6]. In particular, we describe the • locally uniform Poisson behavior of the rescaled eigenvalues, • independence of the Poisson processes obtained as such limits at distinct energies, • locally uniform Poisson behavior of the joint distributions of the rescaled energies and rescaled localization centers in a large range of scales. • the distribution of the rescaled level spacings, locally and globally in energy, • the distribution of the rescaled localization centers spacings. Our results show, in particular, that, for the discrete Anderson Hamiltonian with smoothly distributed random potential at sufficiently large coupling, the limit of the level spacing distribution is that of i.i.d. random variables distributed according to the density of states of the random Hamiltonian.
منابع مشابه
شبیه سازی اثر بی نظمی و میدان مغناطیسی بر ترابرد کوانتومی نانوساختارهای دو بعدی مدل شده با تقریب تنگابست
In recent years, semiconductor nanostructures have become the model systems of choice for investigation of electrical conduction on short length scales. Quantum transport is studied in a two dimensional electron gas because of the combination of a large Fermi wavelength and large mean free path. In the present work, a numerical method is implemented in order to contribute to the understanding ...
متن کاملDilations, models, scattering and spectral problems of 1D discrete Hamiltonian systems
In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a self...
متن کاملDecorrelation estimates for the eigenlevels of the discrete Anderson model in the localized regime
متن کامل
Back-calculation of mechanical parameters of shell and balls materials from discrete element method simulations
Discrete Element Method (DEM) is extensively used for mathematical modeling and simulating the behavior of discrete discs and discrete spheres in two and three dimensional space, respectively. Prediction of particles flow regime, power draw and kinetic energy for a laboratory or an industrial mill is possible by DEM simulation. In this article, a new approach was used to assess the main paramet...
متن کاملRandom Schrödinger Operators: Universal Localization, Correlations, and Interactions
(in alphabetic order by speaker surname) Speaker: Boumaza, Hakim (Keio University) Title: Localization for a matrix-valued Anderson-Bernoulli model Abstract: We will present a localization result, both in the exponential and dynamical senses, for a random, matrix-valued, one-dimensional continuous Schrödinger operator acting on L2(R)⊗ CN , N ≥ 1. For this, we combine results of Klein, Lacroix a...
متن کامل