相关论文: A Single Slice 2d Anderson Model at Weak Disorder

In this paper we describe a strategy to study the Anderson model of an electron in a random potential at weak coupling by a renormalization group analysis. There is an interesting technical analogy between this problem and the theory of…

A new approach is applied to the 1D Anderson model by making use of a two-dimensional Hamiltonian map. For a weak disorder this approach allows for a simple derivation of correct expressions for the localization length both at the center…

In recent years,constructive field techniques and the method of renormalization group around extended singularities have been applied to the weak coupling regime of the Anderson Model. It has allowed to clarify the relationship between this…

This work proposes a very simple random matrix model, the Flip Matrix Model, liable to approximate the behavior of a two dimensional electron in a weak random potential. Its construction is based on a phase space analysis, a suitable…

We explore the properties of discrete random Schroedinger operators in which the random part of the potential is supported on a sub-lattice. In particular, we provide new conditions on the sub-lattice under which Anderson localisation…

The Anderson model in one dimension is a quantum particle on a discrete chain of sites with nearest-neighbor hopping and random on-site potentials. It is a progenitor of many further models of disordered systems, and it has spurred numerous…

We develop a polymer expansion with large/small field conditions for the mean resolvent of a weakly disordered system. Then we show that we can apply our result to a two-dimensional model, for energies outside the unperturbed spectrum or in…

We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…

We present a full analytical solution for the localisation length in the one-dimensional Anderson model with weak diagonal disorder in the vicinity of the band centre. The results are obtained with the Hamiltonian map approach that turns…

Previous work proposed a strong-disorder renormalization approach for the Anderson model, using it to calculate the density of states and the inverse participation ratio [Johri \& Bhatt, Phys.\ Rev.\ B {\bf 90} 060205(R) (2014)]. This is…

It has previously been shown that ordinary least squares can be used to estimate the coefficients of the single-index model under only mild conditions. However, the estimator is non-robust leading to poor estimates for some models. In this…

We develop a discrete version of paracontrolled distributions as a tool for deriving scaling limits of lattice systems, and we provide a formulation of paracontrolled distribution in weighted Besov spaces. Moreover, we develop a systematic…

We show that the Anderson model has a transition from localization to delocalization at exactly 2 dimensional growth rate on antitrees with normalized edge weights which are certain discrete graphs. The kinetic part has a one-dimensional…

This work introduces, analyzes and demonstrates an efficient and theoretically sound filtering strategy to ensure the condition of the least-squares problem solved at each iteration of Anderson acceleration. The filtering strategy consists…

We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional…

We demonstrate the effectiveness of a generalized renormalized perturbational approach to calculate the induced magnetization for the single impurity Anderson model with a strong on-site interaction, using flow equations for renormalized…

Matrix models of 2D quantum gravity are either exactly solvable for matter of central charge $ c\leq 1, $ or not understood. It would be useful to devise an approximate scheme which would be reasonable for the known cases and could be…

In the literature on slice analysis in the hypercomplex setting, there are two main approaches to define slice regular functions in one variable: one consists in requiring that the restriction to any complex plane is holomorphic (with the…

Based on distributions of local Green's functions we present a stochastic approach to disordered systems. Specifically we address Anderson localisation and cluster effects in binary alloys. Taking Anderson localisation of Holstein polarons…

We develop a new approach for the Anderson localization problem. The implementation of this method yields strong numerical evidence leading to a (surprising to many) conjecture: The two dimensional discrete random Schroedinger operator with…