We study compact finite difference methods for the Schrödinger-Poisson equation in a bounded domain and establish their optimal error estimates under proper regularity assumptions on wave function ψ and external potential V(x). The CrankNicolson compact finite difference method and the semi-implicit compact finite difference method are both of order O(h4+τ2) in discrete l2 ,H1 and l norms with ...

Non-Markovian stochastic Langevin-like equations of motion are compared to their corresponding Markovian (local) approximations. The validity of the local approximation for these equations, when contrasted with the fully nonlocal ones, is analyzed in detail. The conditions for when the equation in a local form can be considered a good approximation are then explicitly specified. We study both t...

Micron size dust particles influence on nonlocal properties of complex gas discharge plasma are simulated. Plasma is described within limits of diffusion approximation, combined with OML approximation for dust component. The current-voltage characteristics as the easy-to-observe measure of dust influence on the total amount of charged particles, as well as the radial distributions of plasma com...

We introduce an extension of the dynamical mean-field approximation ~DMFA! that retains the causal properties and generality of the DMFA, but allows for systematic inclusion of nonlocal corrections. Our technique maps the problem to a self-consistently embedded cluster. The DMFA ~exact result! is recovered as the cluster size goes to 1 ~infinity!. As a demonstration, we study the Falicov-Kimbal...

We construct self-similar functions and linear operators to deduce a self-similar variant of the Laplacian operator and of the D'Alembertian wave operator. The exigence of self-similarity as a symmetry property requires the introduction of nonlocal particle-particle interactions. We derive a self-similar linear wave operator describing the dynamics of a quasicontinuous linear chain of infinite ...

We explore the combination of the extended dynamical mean field theory (EDMFT) with the GW approximation (GWA); the former sums the local contributions to the self-energies to infinite order in closed form and the latter handles the nonlocal ones to lowest order. We investigate the different levels of self-consistency that can be implemented within this method by comparing to the exact quantum ...

We discuss a possible form for a theory akin to local density functional theory, but able to produce van der Waals energies in a natural fashion. The usual Local Density Approximation (LDA) for the exchange and correlation energy Exc of an inhomogeneous electronic system can be derived by making a quasilocal approximation for the interacting density-density response function χ(~r, ~r , ω), then...