Related papers: Level Spacing for Non-Monotone Anderson Models
We provide a characterization of the spectral minimum for a random Schr\"odinger operator of the form $H=-\Delta + \sum_{i \in \Z^d}q(x-i-\omega_i)$ in $L^2(\R^d)$, where the single site potential $q$ is reflection symmetric, compactly…
In this work we demonstrate that non-random mechanisms that lead to single-particle localization may also lead to many-body localization, even in the absence of disorder. In particular, we consider interacting spins and fermions in the…
We establish the complete spectral exponential, and the strong Hilbert-Schmidt dynamical localization for the one-dimensional multi-particle Anderson tight-binding model and for weakly interacting particles system. In other words, we show…
Topic of the thesis is a theoretical description of the ultracold atomic gases in one- and two-dimensional optical lattices in the presence of the disorder leading to the Anderson localization. The disorder is created by interaction of the…
The Anderson model serves to study the absence of wave propagation in a medium in the presence of impurities, and is one of the most studied examples in the theory of quantum disordered systems. In these notes we give a review of the…
We consider a two-particle quantum systems in a d-dimensional Euclidean space with interaction and in presence of a random external potential (a continuous two-particle Anderson model). We establish Wegner-type estimates (inequalities) for…
We obtain analytic formulae for the spacing between conductance peaks in the Coulomb blockade regime, based on the universal Hamiltonian model of quantum dots. New random matrix theory results are developed in order to treat correlations…
We consider the Anderson model on the finite grid $G = \mathbb Z/L_1\mathbb Z\times\cdots\times\mathbb Z/L_d\mathbb Z$, defined by the random Hamiltonian $H_t=\Delta+tV$, where $\Delta$ is the discrete Laplacian and…
The localization subregions of stationary waves in continuous disordered media have been recently demonstrated to be governed by a hidden landscape that is the solution of a Dirichlet problem expressed with the wave operator. In this…
Localization properties of non-interacting quantum particles in one-dimensional incommensurate lattices are investigated with an exponential short-range hopping that is beyond the minimal nearest-neighbor tight-binding model. Energy…
We prove the existence of extensive many-body Hamiltonians with few-body interactions and a many-body mobility edge: all eigenstates below a nonzero energy density are localized in an exponentially small fraction of "energetically allowed…
We study localisation effects of strong disorder on the spectral and dynamical properties of (matrix and scalar) Schroedinger operators with non-monotone random potentials, on the d-dimensional lattice. Our results include dynamical…
We study Anderson and alloy type random Schr\"odinger operators on $\ell^2(\ZZ^d)$ and $L^2(\RR^d)$. Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of…
We present some new theoretical and computational results for the stationary points of bulk systems. First we demonstrate how the potential energy surface can be partitioned into catchment basins associated with every stationary point using…
Single-particle transport in disordered potentials is investigated on scales below the localization length. The dynamics on those scales is concretely analyzed for the 3-dimensional Anderson model with Gaussian on-site disorder. This…
We study eigenvalue spacings and local eigenvalue statistics for 1D lattice Schrodinger operators with Holder regular potential, obtaining a version of Minami's inequality and Poisson statistics for the local eigenvalue spacings. The main…
This paper is a complement to our earlier work \cite{BCSS10b}. With the help of the multi-scale analysis, we derive, from estimates obtained in \cite{BCSS10b}, dynamical localization for a multi-particle Anderson model in a Euclidean space…
We prove localization at the bottom of the spectrum for a random Schr\"odinger operator in the continuum with a single-site potential probability distribution supported by a Cantor set of zero Lebesgue measure. This distribution is too…
We compute the distribution function of single-level curvatures, $P(k)$, for a tight binding model with site disorder, on a cubic lattice. In metals $P(k)$ is very close to the predictions of the random-matrix theory (RMT). In insulators…
We develop an alternative scaling approach to determine the criteria for Anderson localization in one-dimensional tight-binding models with random site energies having a bandwidth that decays as a power law in space, $H_{ij} \propto |i -…