Related papers: Rigorous Formalization of Orbital Functionals: Add…

In modeling low-dimensional electronic nanostructures, the evaluation of the electron-electron interaction is a challenging task. Here we present an accurate and practical density-functional approach to the two-dimensional many-electron…

Density functional theory offers accurate structure prediction at acceptable computational cost, but commonly used approximations suffer from delocalization error; this results in inaccurate predictions of quantities such as energy band…

Exact density-functional theory is reconstructed here from its convex variational structure as two parallel exact ensemble hierarchies: an interacting hierarchy rooted in Lieb's ensemble formulation and a noninteracting hierarchy rooted in…

We ask what happens when the index set carries modal structure, with possibilities organized into a Kripke frame. We define modal exchangeability as invariance under accessibility-preserving automorphisms that fix a designated base world,…

In this article, we present a formalization of spherically complete spaces, which is a fundamental notion in non-archimedean functional analysis. This work includes the equivalent definitions of spherically complete spaces, their basic…

In this paper I explore the relationship between regular functions associated to local systems on nilpotent orbits and unipotent representations in the complex groups.

We describe in detail the method used in our previous work arXiv:1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal…

While in principle exact, Kohn-Sham density functional theory -- the workhorse of computational chemistry -- must rely on approximations for the exchange-correlation functional. Despite staggering successes, present-day approximations still…

In the exact Kohn-Sham density-functional theory (DFT), the total energy versus the number of electrons is a series of linear segments between integer points. However, commonly used approximate density functionals produce total energies…

The practical success of density functional theory (DFT) is largely credited to the Kohn-Sham approach, which enables the exact calculation of the non-interacting electron kinetic energy via an auxiliary noninteracting system. Yet, the…

We present a Representer Theorem result for a large class of weak formulation problems. We provide examples of applications of our formulation both in traditional machine learning and numerical methods as well as in new and emerging…

The nongeneric six- and eightdimensional orbits of SO(4,2) are described in explicitly covariant way. The relevant Hamiltonian dynamical systems are constructed and canonically quantized. It is shown that the resulting unitary…

In this paper, we obtain some important variants of the Lions and Chabrowski Concentration-compactness principle, in the context of fractional Sobolev spaces with variable exponents, especially for nonlinear systems. As an application of…

The occupation of d-orbitals controls the magnitude and anisotropy of the inter-atomic electron transfer in transition metal oxides and hence exerts a key influence on their chemical bonding and physical properties. Atomic-scale modulations…

We report equations of motion for the occupation numbers of natural spin orbitals and show that adiabatic extensions of common functionals employed in ground-state reduced-density-matrix-functional theory have the shortcoming of leading…

A simple and completely general representation of the exact exchange-correlation functional of density-functional theory is derived from the universal Lieb-Oxford bound, which holds for any Coulomb-interacting system. This representation…

Let $G$ be a classical linear algebraic group over an algebraically closed field, and let $\mathfrak{n}$ denote the subset of nilpotent elements in its Lie algebra. In this paper we study a partial order on the $G$-orbits in $\mathfrak{n}$…

In the first part of this thesis we study the generalization of the recent algebraic approach to classical field theory by proposing a more general setting based on the manifold of smooth sections of a non-trivial fiber bundle. Central is…

The general procedure underlying Hartree-Fock and Kohn-Sham density functional theory calculations consists in optimizing orbitals for a self-consistent solution of the Roothaan-Hall equations in an iterative process. It is often ignored…

We re-adapt a spectral renormalization method, introduced in nonlinear optics, to solve the Kohn-Sham (KS) equations of density functional theory (DFT), with a focus on functionals based on the strictly-correlated electrons (SCE) regime,…