Related papers: Simplicity of eigenvalues in the Anderson model
We prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.
We present a method of cones for rigorous estimations of eigenvectors, eigenspaces and eigenvalues of a matrix. The key notion is the cone-domination and is inspired by ideas from hyperbolic dynamical systems. We present theorems which…
A non-perturbative local moment approach to single-particle dynamics of the general asymmetric Anderson impurity model is developed. The approach encompasses all energy scales and interaction strengths. It captures thereby strong coupling…
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…
For a non-local semilinear eigenvalue problem, we prove simplicity and isolation of the first eigenvalue with homogeneous Dirichlet boundary conditions on open sets supporting a suitable compact Sobolev embedding.
Mirsky proved that, for the existence of a complex matrix with given eigenvalues and diagonal entries, the obvious necessary condition is also sufficient. We generalize this theorem to matrices over any field and provide a short proof.…
In linear disordered systems Anderson localization makes any wave packet stay localized for all times. Its fate in nonlinear disordered systems is under intense theoretical debate and experimental study. We resolve this dispute showing that…
We examine the use of distributions in numerical treatments of Anderson localisation and supply evidence that treating exponential localisation on Bethe lattices recovers the overall picture known from hypercubic lattices in 3d.
Recently we found an Anderson-type localization-delocalization transition in the QCD Dirac spectrum at high temperature. Using spectral statistics we obtained a critical exponent compatible with that of the corresponding Anderson model.…
The wave function of a non-relativistic particle in a periodic potential admits oscillatory solutions, the Bloch waves. In the presence of a random noise contribution to the potential the wave function is localized. We outline a new proof…
We propose a technique for calculating and understanding the eigenvalue distribution of sums of random matrices from the known distribution of the summands. The exact problem is formidably hard. One extreme approximation to the true density…
Simple-minded systems in stable module categories are defined by orthogonality and generating properties so that the images of the simple modules under a stable equivalence form such a system. Simple-minded systems are shown to be invariant…
We present a generalization of the method of the local relaxation flow to establish the universality of local spectral statistics of a broad class of large random matrices. We show that the local distribution of the eigenvalues coincides…
Let $\mu_1$ be a complex number in the numerical range $W(A)$ of a normal matrix $A$. In the case when no eigenvalues of $A$ lie in the interior of $W(A)$, we identify the smallest convex region containing all possible complex numbers…
This paper provides an overview of the necessary and sufficient conditions for guaranteeing the unique solvability of absolute value equations. In addition to discussing the basic form of these equations, we also address several…
We consider a two dimensional magnetic Schroedinger operator on a square lattice with a spatially stationary random magnetic field. We prove Anderson localization near the spectral edges. We use a new approach to establish a Wegner estimate…
Following [5], we analyze regularity properties of single-site probability distributions of the random potential and of the Integrated Density of States (IDS) in the Anderson models with infinite-range interactions. In the present work, we…
Two simple, interpolatory-like linearizations are shown for the simple pendulum which can be used for any initial amplitude.
The aim of this work is to extend the results from [B2] on local eigenvalue spacings to certain 1D lattice Schrodinger with a Bernoulli potential. We assume the disorder satisfies a certain algebraic condition that enables one to invoke the…
We prove that an n by n random matrix G with independent entries is completely delocalized. Suppose the entries of G have zero means, variances uniformly bounded below, and a uniform tail decay of exponential type. Then with high…