Exact Density Functionals in One Dimension

TL;DR

This paper introduces a new method for deriving exact density functionals in one-dimensional lattice gases with finite-range interactions, using a generalized Markov property, and discusses implications for higher-dimensional systems.

Contribution

It presents a general, transparent scheme for deriving exact density functionals in 1D systems, unifying previous results and suggesting pathways for higher-dimensional approximations.

Findings

Unified framework for exact 1D density functionals

Derivation of continuum functionals via limiting procedures

Implications for constructing approximate functionals in higher dimensions

Abstract

We propose a new and general method for deriving exact density functionals in one dimension for lattice gases with finite-range pairwise interactions. Corresponding continuum functionals are derived by applying a proper limiting procedure. The method is based on a generalised Markov property, which allows us to set up a rather transparent scheme that covers all previously known exact functionals for one-dimensional lattice gas or fluid systems. Implications for a systematic construction of approximate density functionals in higher dimensions are pointed out.