First order expansion in the semiclassical limit of the Levy-Lieb functional

2021/06/11 by Maria Colombo, Simone Di Marino, Colombo, Maria +3
Mathematics · Physics and Astronomy · #35B25 #35J10 #35Q70 #49Q22 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2106.06282

openalex publication_date 2021/06/11 · openalex created_date 2021/06/22 · openalex updated_date 2026/07/28

Abstract

We prove the conjectured first order expansion of the Levy-Lieb functional in the semiclassical limit, arising from Density Functional Theory (DFT). This is accomplished by interpreting the problem as the singular perturbation of an Optimal Transport problem via a Dirichlet penalization.

Related

• Semi-classical limit of the Levy-Lieb functional in Density Functional Theory
• Convergence of Levy-Lieb to Thomas-Fermi density functional
• The Lieb-Oxford bound and the optimal transport limit of DFT
• A sparse approximation of the Lieb functional with moment constraints
• Exact Constraint of Density Functional Approximations at the Semiclassical Limit