The design of Kinetic Functionals for Many-Body Electron Systems : Combining analytical theory with Monte Carlo sampling of electronic configurations

TL;DR

This paper develops a computational approach combining analytical kinetic functionals with Monte Carlo sampling to create accurate, local kinetic functionals for many-electron systems, improving numerical applicability.

Contribution

It introduces a novel method that integrates analytical theory with Monte Carlo sampling to design local kinetic functionals for many-electron systems.

Findings

The proposed scheme is internally consistent.

It effectively combines analytical and numerical methods.

The approach improves the design of local kinetic functionals.

Abstract

In a previous work [L.Delle Site, J.Phys.A 40, 2787 (2007)] the derivation of an analytic expression for the kinetic functional of a many-body electron system has been proposed. Though analytical, the formula is still non local (multidimensional) and thus not ideal for numerical applications. In this work, by treating the test case of a uniform gas of interacting spinless electrons, we propose a computational protocol which combines the previous analytic results with the Monte Carlo (MC) sampling of electronic configurations in space. This, we show, leads to an internally consistent scheme to design well founded local kinetic functionals.