Related papers: Fractional Moment Methods for Anderson Localizatio…
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…
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 prove spectral and dynamical localization for Anderson models on locally finite graphs using the fractional moment method. Our theorems extend earlier results on localization for the Anderson model on $\ZZ^d$. We establish geometric…
The fractional moment method, which was initially developed in the discrete context for the analysis of the localization properties of lattice random operators, is extended to apply to random Schr\"odinger operators in the continuum. One of…
Mathematical analysis of the Anderson localization has been facilitated by the use of suitable fractional moments of the Green function. Related methods permit now a readily accessible derivation of a number of physical manifestations of…
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…
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…
We give a widely self-contained introduction to the mathematical theory of the Anderson model. After defining the Anderson model and determining its almost sure spectrum, we prove localization properties of the model. Here we discuss…
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…
We present a new, short, self-contained proof of localization properties of multi-dimensional continuum random Schr\"odinger operators in the fluctuation boundary regime. Our method is based on the recent extension of the fractional moment…
A general formula for the orbital magnetic moment of interacting electrons in solids is derived using the many-electron Green function method. The formula factorizes into two parts, a part that contains the information about the…
We review the description and modeling of transport phenomena among the electron systems coupled via scalar or vector photons. It consists of three parts. The first part is about scalar photons, i.e., Coulomb interactions. The second part…
The asymptotics of n-point Green's function at large external momenta is obtained in the exponentiated form using the Fock-Feynman-Schwinger representation for propagators in the external field. The method is applied to gauge theories such…
This paper is a follow-up of our recent papers \cite{CS08} and \cite{CS09} covering the two-particle Anderson model. Here we establish the phenomenon of Anderson localisation for a quantum $N$-particle system on a lattice $\Z^d$ with…
We prove a connection between the Green's function of the fractional Anderson model and the two point function of a self-avoiding random walk with long range jumps, adapting a strategy proposed by Schenker in 2015. This connection allows us…
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…
This paper establishes dynamical localization properties of certain families of unitary random operators on the d-dimensional lattice in various regimes. These operators are generalizations of one-dimensional physical models of quantum…
We consider unitary analogs of $d-$dimensional Anderson models on $l^2(\Z^d)$ defined by the product $U_\omega=D_\omega S$ where $S$ is a deterministic unitary and $D_\omega$ is a diagonal matrix of i.i.d. random phases. The operator $S$ is…
In this paper, a method for autonomous segmentation of demonstrated robot movements is proposed. Position data is clustered into Gaussian mixture models (GMMs), and an initial set of segments is identified from the Gaussian basis functions.…
In this paper we evaluate the expression for the Green function of a pseudo-classical spinning particle interacting with constant electromagnetic external fields by taking into account the anomalous magnetic and electric moments of the…