Work

First Order Expansion in the Semiclassical Limit of the Levy–Lieb Functional

Year: 2025

Type: article

Abstract: We prove the conjectured first order expansion of the Levy-Lieb functional in the semiclassical limit, arising from Density Functional Theory (DFT). In particular, we prove a general asymptotic first order lower bound in terms of the zero point oscillation functional and the corresponding asymptotic upper bound in the case of two electrons in one dimension. This is accomplished by interpreting the problem as the singular perturbation of an Optimal Transport problem via a Dirichlet penalization.

Source: Archive for Rational Mechanics and Analysis

DOI: 10.1007/s00205-025-02143-7

Authors: Maria Colombo, Simone Di Marino, Federico Stra

Institutions: École Polytechnique Fédérale de Lausanne, University of Genoa, Politecnico di Torino

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090