Related papers: Localization for random operators on $\mathbb{Z}^d…
We investigate the sample paths regularity of operator scaling alpha-stable random fields. Such fields were introduced as anisotropic generalizations of self-similar fields and satisfy a scaling property for a real matrix E. In the case of…
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…
The purpose of the present work is to establish decorrelation estimates for some random discrete Schrodinger operator in dimension one. We prove that the Minami estimates are consequences of the Wegner estimates and Localization. We also…
We establish strong dynamical localization for a class of multi-particle Anderson models in a Euclidean space with an alloy-type random potential and a sub-exponentially decaying interaction of infinite range. For the first time in the…
The paper deals with homogenization of divergence form second order parabolic operators whose coefficients are periodic in spatial variables and random stationary in time. Under proper mixing assumptions, we study the limit behaviour of the…
A finite number of harmonic oscillators coupled to infinitely many environment oscillators is fundamental to the problem of understanding quantum dissipation of a small system immersed in a large environment. Exact operator solution as a…
We consider a random time evolution operator composed of a circuit of random unitaries coupling even and odd neighboring spins on a chain in turn. In spirit of Floquet evolution, the circuit is time-periodic; each timestep is repeated with…
We study multi-frequency quasi-periodic Schr\"odinger operators on $\mathbb{Z}$ in the regime of positive Lyapunov exponent and for general analytic potentials. Combining Bourgain's semi-algebraic elimination of multiple resonances with the…
We investigate the localization of electrons hopping on quasi-1D strips in the presence of random magnetic field. In the weak-disorder region, by perturbative analytical techniques, we derive scaling laws for the localization length,…
We consider Schr\"odinger operator with random decaying potential on $\ell^2 ({\bf Z}^d)$ and showed that, (i) IDS coincides with that of free Laplacian in general cases, and (ii) the set of extremal eigenvalues, after rescaling, converges…
This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic…
This article establishes a proof of dynamical localization for a random scattering zipper model. The scattering zipper operator is the product of two unitary by blocks operators, multiplicatively perturbed on the left and right by random…
We study the spatial decay of eigenfunctions of non-local Schr\"odinger operators whose kinetic terms are generators of symmetric jump-paring L\'evy processes with Kato-class potentials decaying at infinity. This class of processes has the…
We prove local bounds on the amplitude of eigen- functions of complex constant-coefficient elliptic operators with a smooth potential on an arbitrary open subset of \R^d by estimating it in terms of the number of solutions of a diophantine…
We study discrete magnetic random Schr\"odinger operators on the square and honeycomb lattice. For the non-random magnetic operator on the hexagonal lattice with any rational magnetic flux, we show that the middle two dispersion surfaces…
We consider a d-dimensional random quantum walk with site-dependent random coin operators. The corresponding transition coefficients are characterized by deterministic amplitudes times independent identically distributed site-dependent…
We study localization properties of electronic states in one-dimensional lattices with nearest-neighbour interaction. Both the site energies and the hopping amplitudes are supposed to be of arbitrary form. A few cases are considered in…
We investigate a paradigmatic model for quantum transport with both nearest-neighbor and infinite range hopping coupling (independent of the position). Due to long range homogeneous hopping, a gap between the ground state and the excited…
We study the approximation properties of pseudo-differential operators with small time-frequency dispersion, meaning that their spreading functions are supported in a small neighborhood of the origin. It is commonly assumed that for such…
With a tight binding treatment we examine amorphous conductors with gas-like disorder, or no correlations among the site positions. We consider an exponentially decaying hopping integral with range $l$, and the Inverse Participation Ratio…