Related papers: Numerical methods for localization
We study Anderson localization of ultracold atoms in weak, one-dimensional speckle potentials, using perturbation theory beyond Born approximation. We show the existence of a series of sharp crossovers (effective mobility edges) between…
Anderson localization of classical waves in disordered media is a fundamental physical phenomenon that has attracted attention in the past three decades. More recently, localization of polar excitations in nanostructured metal-dielectric…
We prove localization (near the bottom of the spectrum) for certain non-stationary variants of the Anderson model in three dimensions. More specifically, we prove a Wegner estimate, which implies localization by existing work. Two key…
We prove a Wegner estimate for a large class of multiparticle Anderson Hamiltonians on the lattice. These estimates will allow us to prove Anderson localization for such systems. A detailed proof of localization will be given in a…
The localization of one-electron states in the large (but finite) disorder limit is investigated. The inverse participation number shows a non--monotonic behavior as a function of energy owing to anomalous behavior of few-site localization.…
Anderson acceleration is a well-established and simple technique for speeding up fixed-point computations with countless applications. Previous studies of Anderson acceleration in optimization have only been able to provide convergence…
We extend the concept of Anderson localization, the confinement of quantum information in a spatially irregular potential, to quantum circuits. Considering matchgate circuits, generated by time-dependent spin-1/2 XY Hamiltonians, we give an…
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…
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…
In a recent publication, J. Phys.: Condens. Matt. 14 13777 (2002), Kuzovkov et. al. announced an analytical solution of the two-dimensional Anderson localisation problem via the calculation of a generalised Lyapunov exponent using signal…
The self-consistent theory of localization is generalized to account for a weak quadratic nonlinear potential in the wave equation. For spreading wave packets, the theory predicts the destruction of Anderson localization by the nonlinearity…
This paper is a contribution to the problem of particle localization in non-relativistic Quantum Mechanics. Our main results will be (1) to formulate the problem of localization in terms of invariant subspaces of the Hilbert space, and (2)…
Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results. We survey developments in the area both from the algorithmic and…
We study spectral properties of partial differential operators modelling composite materials with highly contrasting constituents, comprised of soft spherical inclusions with random radii dispersed in a stiff matrix. Such operators have…
We introduce deterministic perturbation schemes for the recently proposed random directions stochastic approximation (RDSA) [17], and propose new first-order and second-order algorithms. In the latter case, these are the first second-order…
We reply to comments by P.Marko$\breve{s}$, L.Schweitzer and M.Weyrauch [preceding paper] on our recent paper [J. Phys.: Condens. Matter 63, 13777 (2002)]. We demonstrate that our quite different viewpoints stem for the different physical…
Motivated by current interest in disordered systems of interacting electrons, the effectiveness of the geometrically averaged density of states, $\rho_g(\omega)$, as an order parameter for the Anderson transition is examined. In the context…
The problem of two electrons in a two-dimensional random potential is addressed numerically. Specifically, the role of the Coulomb interaction between electrons on localization is investigated by writing the Hamiltonian on a localized basis…
A solid transparent medium with randomly positioned, immobile impurity atoms is a promising candidate for observation of Anderson localization of light in three dimensions. It can have low losses and allows for mitigation of the detrimental…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…