相关论文: Remarks on the semi-classical Hohenberg-Kohn funct…

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…

We prove rigorously that the exact N-electron Hohenberg-Kohn density functional converges in the strongly interacting limit to the strictly correlated electrons (SCE) functional, and that the absolute value squared of the associated…

We adapt the problem of continuous congested optimal transport to the Heisenberg group, equipped with a sub-Riemannian metric. Originally introduced in the Euclidean setting by Carlier, Jimenez, and Santambrogio as a path-dependent variant…

The optimal transport problem is studied in the context of Lorentz-Finsler geometry. For globally hyperbolic Lorentz-Finsler spacetimes the first Kantorovich problem and the Monge problem are solved. Further the intermediate regularity of…

We study the optimal transport problem in sub-Riemannian manifolds where the cost function is given by the square of the sub-Riemannian distance. Under appropriate assumptions, we generalize Brenier-McCann's Theorem proving existence and…

We derive quantum Boltzmann equations from Schwinger-Dyson equations in gradient expansion for a weakly coupled scalar field theory with a spatially varying mass. We find that at higher order in gradients a full description of the system…

A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…

We present here novel insight into exchange-correlation functionals in density functional theory, based on the viewpoint of optimal transport. We show that in the case of two electrons and in the semiclassical limit, the exact…

We consider an optimal transport problem on the unit simplex whose solutions are given by gradients of exponentially concave functions and prove two main results. First, we show that the optimal transport is the large deviation limit of a…

Motivated by applications to geometric inequalities, Gozlan, Roberto, Samson, and Tetali introduced a transport problem for `weak' cost functionals. Basic results of optimal transport theory can be extended to this setup in remarkable…

We introduce a formulation of optimal transport problem for distributions on function spaces, where the stochastic map between functional domains can be partially represented in terms of an (infinite-dimensional) Hilbert-Schmidt operator…

We derive and analyze a hierarchy of approximations to the strongly correlated limit of the Hohenberg-Kohn functional. These "density representability approximations" are obtained by first noting that in the strongly correlated limit,…

We study the semi-discrete formulation of one-dimensional partial optimal transport with quadratic cost, where a probability density is partially transported to a finite sum of Dirac masses of smaller total mass. This problem arises…

The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…

Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we solve analytically a one-dimensional fractional diffusion-advection equation for the particle density. We…

Given a vector space of microscopic quantum observables, density functional theory is formulated on its dual space. A generalized Hohenberg-Kohn theorem and the existence of the universal energy functional in the dual space are proven. In…

The most challenging scenario for Kohn-Sham density functional theory, that is when the electrons move relatively slowly trying to avoid each other as much as possible because of their repulsion (strong-interaction limit), is reformulated…

An optimal transport problem on finite spaces is a linear program. Recently, a relaxation of the optimal transport problem via strictly convex functions, especially via the Kullback--Leibler divergence, sheds new light on data sciences.…

The paper considers a class of linear Boltzmann transport equations which models a charged particle transport. The equation is an approximation of the original exact transport equation which involves hyper-singular integrals in their…

We present a minimization problem with a horizontal divergence-type constraint in the Heisenberg group. Our study explores its dual formulation and examines its relationship with the congested optimal transport problem, for $1 < p <…