相关论文: Semi-classical limit of the Levy-Lieb functional i…
We prove that the Levy-Lieb density functional Gamma-converges to the Thomas-Fermi functional in the semiclassical mean-field limit. In particular, this aides an easy alternative proof of the validity of the atomic Thomas-Fermi theory which…
The constrained-search formulation of Levy and Lieb provides a concrete mapping from N-representable densities to the space of N-particle wavefunctions and explicitly defines the universal functional of density functional theory. We…
In this paper the classical limit of relativistic transport theories for spin 1/2 fermions is examined through a comparison with the classical kinetic theory derived from N=1 supersymmetric classical mechanics. The conclusion is that in the…
In this chapter we first review the Levy-Lieb functional, which gives the lowest kinetic and interaction energy that can be reached with all possible quantum states having a given density. We discuss two possible convex generalizations of…
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…
We present some progress in the direction of determining the semiclassical limit of the Hoenberg-Kohn universal functional in Density Functional Theory for Coulomb systems. In particular we give a proof of the fact that for Bosonic systems…
In the semi-classical limit, the quantum mechanics of a stationary beam of counter-streaming relativistic electrons and ions is described by a nonlinear system of finite-temperature Thomas-Fermi equations. In the high temperature / low…
In the full quantum theory, the energy of a many-body quantum system with a given one-body density is described by the Levy-Lieb functional. It is exact, but very complicated to compute. For practical computations, it is useful to introduce…
The functional method to derive the fractional Fokker-Planck equation for probability distribution from the Langevin equation with Levy stable noise is proposed. For the Cauchy stable noise we obtain the exact stationary probability density…
The aim of this paper is to present new sparsity results about the so-called Lieb functional, which is a key quantity in Density Functional Theory for electronic structure calculations of molecules. The Lieb functional was actually shown by…
A generalization of the Density Functional Theory is proposed. The theory developed leads to single-particle equations of motion with a quasi-local mean-field operator, which contains a quasi-particle position-dependent effective mass and a…
The importance of the Lieb-Simon proof of the relative exactness of Thomas-Fermi theory in the large-Z limit to modern density functional theory (DFT) is explored. The principle, that there is a specific semiclassical limit in which…
Potential functional approximations are an intriguing alternative to density functional approximations. The potential functional that is dual to the Lieb density functional is defined and properties given. The relationship between…
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 question of whether given density operators for subsystems of a multipartite quantum system are compatible to one common total density operator is known as the quantum marginal problem. We briefly review the solution of a subclass of…
We give the first mathematically rigorous justification of the Local Density Approximation in Density Functional Theory. We provide a quantitative estimate on the difference between the grand-canonical Levy-Lieb energy of a given density…
Our goal in this paper is twofold. First, we characterize the class of pairwise interactions for which the Seidl conjecture on the structure of optimal plans for the symmetric multimarginal optimal transport problem with one-dimensional…
In this paper, we rewrite the time-dependent Bogoliubov$\unicode{x2013}$de Gennes equation in an appropriate semiclassical form and establish its semiclassical limit to a two-particle kinetic transport equation with an effective mean-field…
We study a new class of so-called rational-infinitely (or quasi-infinitely) divisible probability laws on the real line. The characteristic functions of these distributions are ratios of the characteristic functions of classical infinitely…
We review a semi-classical transport theory for non-Abelian plasmas based on a classical picture of coloured point particles. Within this formalism, kinetic equations for the mean particle distribution, the mean fields and their…