Related papers: Localization Bounds for an Electron Gas
A technically convenient signature of localization, exhibited by discrete operators with random potentials, is exponential decay of the fractional moments of the Green function within the appropriate energy ranges. Known implications…
A technically convenient signature of Anderson localization is exponential decay of the fractional moments of the Green function within appropriate energy ranges. We consider a random Hamiltonian on a lattice whose randomness is generated…
We give a proof of dynamical localization in the form of exponential decay of spatial correlations in the time evolution for the one-dimensional continuum Anderson model via the fractional moments method. This follows via exponential decay…
We present a family of finite-volume criteria which cover the regime of exponential decay for the fractional moments of Green functions of operators with random potentials. Such decay is a technically convenient characterization of…
Electrons at the Fermi energy may lose their ability to propagate to long distances in certain random media. We use Green functions and solve parquet equations for the non-local electron-hole vertex in high spatial dimensions to describe…
The existence of Anderson localization, characterized by vanishing diffusion due to strong disorder, has been demonstrated in numerous ways. A systematic approach based on the Anderson quantum model of the Fermi gas in random lattices that…
Using a finite-size scaling method, we calculate the localization properties of a disordered two-dimensional electron system in the presence of a random magnetic field. Below a critical energy $E_c$ all states are localized and the…
The interplay between interaction and disorder-induced localization is of fundamental interest. This article addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative…
One of the fundamental results in the theory of localization for discrete Schr\"odinger operators with random potentials is the exponential decay of Green's function and the absence of continuous spectrum. In this paper we provide a new…
For Anderson Localization models with multifractal eigenvectors on disordered samples containing $N$ sites, we analyze in a unified framework the consequences for the statistical properties of the Green function. We focus in particular on…
We consider the spectral and dynamical properties of quantum systems of $n$ particles on the lattice $\Z^d$, of arbitrary dimension, with a Hamiltonian which in addition to the kinetic term includes a random potential with iid values at the…
We present an eigensystem multiscale analysis for proving localization (pure point spectrum with exponentially decaying eigenfunctions, dynamical localization) for the Anderson model in an energy interval. In particular, it yields…
The Green's function contains much information about physical systems. Mathematically, the fractional moment method (FMM) developed by Aizenman and Molchanov connects the Green's function and the transport of electrons in the Anderson…
Exact ground-state properties are presented by combining the diagonalization in the Fock space (and taking all hopping integrals and all two-site interactions) with the ab initio optimization of the Wannier functions. Electrons are…
The decay properties of the one-particle Green function in real space and imaginary time are systematically studied for solids. I present an analytic solution for the homogeneous electron gas at finite and at zero temperature as well as…
We consider the cumulant expansion of the PAM employing the hybridization as perturbation (Phys. Rev. B 50, 17933 (1994)), and we obtain formally exact one-electron Green's functions (GF). These GF contain effective cumulants that are as…
We develop in detail a new formalism [as a sequel to the work of T. Champel and S. Florens, Phys. Rev. B 75, 245326 (2007)] that is well-suited for treating quantum problems involving slowly-varying potentials at high magnetic fields in…
Electron localization is the tendency of an electron in a many-body system to exclude other electrons from its vicinity. Using a new natural measure of localization based on the exact manyelectron wavefunction, we find that localization can…
We review several techniques and ideas initiated by a remarkable work by Spencer [26], used and further developed in numerous subsequent researches. We also describe a relatively short and elementary derivation of the spectral and strong…
Anderson localization has been observed for a variety of media, including ultracold atomic gases with speckle disorder in one and three dimensions. However, observation of Anderson localization in a two-dimensional geometry for ultracold…