How and why could an interacting system of many particles be described as if all particles
were independent and identically distributed? This question is at least as old as statistical …

We consider the implications of the Lieb-Simon limit for correlation in density functional
theory. In this limit, exemplified by the scaling of neutral atoms to large atomic number, local …

Projection operators arise naturally as one-particle density operators associated to Slater
determinants in fields such as quantum mechanics and the study of determinantal …

In this paper we define and study the classical Uniform Electron Gas (UEG), a system of
infinitely many electrons whose density is constant everywhere in space. The UEG is …

In this paper, we investigate the Gibbs measures associated with the focusing nonlinear
Schr\" odinger equation with an anharmonic potential. We establish a dichotomy for …

In this paper, we prove a quantitative version of the semiclassical limit from the Hartree to the
Vlasov equation with singular interaction, including the Coulomb potential. To reach this …

Given 0< s< d 2 with s Ä 1, we are interested in the large N-behavior of the optimal constant
ÄN in the Hardy inequality Pn nD1. n/s ÄN P n< m jXn Xmj 2s, when restricted to …

We study the semiclassical limit from the time-dependent Hartree equation with Coulomb or
gravitational potential to the Vlasov--Poisson equation. We prove convergence in trace norm …

We study the minimizers of an energy functional with a self-consistent magnetic field, which
describes a quantum gas of almost-bosonic anyons in the average-field approximation. For …

We study the time dependent Schrödinger equation for large spinless fermions with the
semiclassical scale ℏ= N^-1/3 ħ= N-1/3 in three dimensions. By using the Husimi measure …