相关论文: Convergence of Levy-Lieb to Thomas-Fermi density f…

We study a system of $N$ fermions in the regime where the intensity of the interaction scales as $1/N$ and with an effective semi-classical parameter $\hbar=N^{-1/d}$ where $d$ is the space dimension. For a large class of interaction…

The semi-classical approach leading to the Thomas-Fermi (TF) model provides a simple universal thermodynamic description of the electronic cloud surrounding the nucleus in an atom. This model is known to be exact at the limit of…

The exact Kohn-Sham iteration of generalized density-functional theory in finite dimensions witha Moreau-Yosida regularized universal Lieb functional and an adaptive damping step is shown toconverge to the correct ground-state density.

We establish some new results about the $\Gamma$-limit, with respect to the $L^1$-topology, of two different (but related) phase-field approximations of the so-called Euler's Elastica Bending Energy for curves in the plane.

Lewin and Lieb have recently proven several new bounds on the exchange-correlation energy that complement the Lieb-Oxford bound. We test these bounds for atoms, for slowly-varying gases, and for Hooke's atom, finding them usually less…

We prove a theorem, using the density functional approach and relying on a classical result by Lieb and Simon on Thomas-Fermi model, showing that in the thermodynamic limit bulk matter is at most semiclassical and coherence preserving. The…

We investigate the particle and kinetic-energy densities for a system of $N$ fermions bound in a local (mean-field) potential $V(\bfr)$. We generalize a recently developed semiclassical theory [J. Roccia and M. Brack, Phys. Rev.\ Lett. {\bf…

Lieb's convex formulation of density-functional theory is presented in a pedagogical manner, emphasizing its connection to Hohenberg-Kohn theory and to Levy's constrained-search theory. The Hohenberg-Kohn and Lieb variation principles are…

Under a suitable notion of equivalence of integral densities we prove a $\Gamma$-closure theorem for integral functionals: The limit of a sequence of $\Gamma$-convergent families of such functionals is again a $\Gamma$-convergent family.…

A density functional theory is developed for fermions in one dimension, interacting via a delta-function. Such systems provide a natural testing ground for questions of principle, as the local density approximation should work well for…

This paper deals with the comparison between the strong Thomas-Fermi theory and the quantum mechanical ground state energy of a large atom confined to lowest Landau band wave functions. Using the tools of microlocal semiclassical spectral…

We establish a framework that allows to prove Gamma-converge of functionals of Lagrangian form on spaces of trajectories based on convergence of viscosity solutions of associated Hamilton-Jacobi equations. Gamma convergence follows from a:…

We prove central limit theorems for additive functionals of stationary fields under integrability conditions on the higher-order spectral densities, which are derived using the Holder-Young-Brascamp-Lieb inequality.

In order to obtain a reasonably accurate and easily implemented approach to many-electron calculations, we will develop a new Density Functional Theory (DFT). Specifically, we derive an approximation to electron density, the first term of…

We present a new semiclassical theory for describing pairing in finite Fermi systems. It is based on taking the $\hbar \to 0$, i.e. Thomas-Fermi, limit of the gap equation written in the basis of the mean field (weak coupling). In addition…

The constrained-search principle introduced by Levy and Lieb, is proposed as a practical, though conceptually rigorous, link between Density Functional Theory (DFT) and Quantum Monte Carlo (QMC). The resulting numerical protocol realizes in…

An effective field approximation, similar to the atomic Thomas-Fermi approach, is proposed for studying non-Abelian gauge theories which includes finite-volume effects. As applications of the formalism the equation of state for an SU(2)…

We study a class of non-local functionals that was introduced by Brezis--Seeger--Van Schaftingen--Yung, and can be used to characterize the total variation of functions. We establish the $\Gamma$-limit of these functionals with respect to…

We analyze the range of validity of Thomas Fermi theory for describing charge density modulations induced by external potentials in neutral graphene. We compare exact results obtained from a tight-binding calculation with those of linear…

The main result of this paper is the rate of convergence to Hermite-type distributions in non-central limit theorems. To the best of our knowledge, this is the first result in the literature on rates of convergence of functionals of random…