Fast localization of eigenfunctions via smoothed potentials

by   Jianfeng Lu, et al.

We study the problem of predicting highly localized low-lying eigenfunctions (-Δ +V) ϕ = λϕ in bounded domains Ω⊂ℝ^d for rapidly varying potentials V. Filoche Mayboroda introduced the function 1/u, where (-Δ + V)u=1, as a suitable regularization of V from whose minima one can predict the location of eigenfunctions with high accuracy. We proposed a fast method that produces a landscapes that is exceedingly similar, can be used for the same purposes and can be computed very efficiently: the computation time on an n × n grid, for example, is merely 𝒪(n^2 logn), the cost of two FFTs.



page 9

page 11

page 12

page 13

page 17


Regularized Potentials of Schrödinger Operators and a Local Landscape Function

We study localization properties of low-lying eigenfunctions (-Δ +V...

Localized Coulomb Descriptors for the Gaussian Approximation Potential

We introduce a novel class of localized atomic environment representatio...

A fast method for evaluating Volume potentials in the Galerkin boundary element method

Three algorithm are proposed to evaluate volume potentials that arise in...

A Dissipation Theory for Potentials-Based FDTD for Lossless Inhomogeneous Media

A dissipation theory is proposed for the potentials-based FDTD algorithm...

On the Approximation of Local Expansions of Laplace Potentials by the Fast Multipole Method

In this paper, we present a generalization of the classical error bounds...

The exponential decay of eigenfunctions for tight binding Hamiltonians via landscape and dual landscape functions

We consider the discrete Schrödinger operator H=-Δ+V on a cube M⊂Z^d, wi...

High Performance Evaluation of Helmholtz Potentials using the Multi-Level Fast Multipole Algorithm

Evaluation of pair potentials is critical in a number of areas of physic...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.