Related papers: Relating the pure and ensemble density matrix func…

Density functional theory, when applied to systems with $T\neq 0$, is based on the grand canonical extension of the Hohenberg-Kohn-Sham theorem due to Mermin (HKSM theorem). While a straightforward canonical ensemble generalization fails,…

We give graphical rules, based on earlier work for the functional Schrodinger equation, for constructing the density matrix for scalar and gauge fields at finite temperature T. More useful is a dimensionally-reduced effective action (DREA)…

We present an ab-initio approach for grand canonical ensembles in thermal equilibrium with local or nonlocal external potentials based on the one-reduced density matrix. We show that equilibrium properties of a grand canonical ensemble are…

We present an \textit{ab initio} theory for superconductors, based on a unique mapping between the statistical density operator at equilibrium, on the one hand, and the corresponding one-body reduced density matrix $\gamma$ and the…

A critical challenge for density functional theory (DFT) in practice is its limited ability to treat static electron correlation, leading to errors in its prediction of charges, multiradicals, and reaction barriers. Recently, we combined…

By a theorem of Greene and Wu, a noncompact connected Riemannian manifold admits a smooth strictly subharmonic exhaustion function. Demailly provided an elementary proof of this fact. A further simplification of Demailly's proof and some…

Ensemble density functional theory (eDFT) is an exact time-independent alternative to time-dependent DFT (TD-DFT) for the calculation of excitation energies. Despite its formal simplicity and advantages in contrast to TD-DFT (multiple…

Density functional theory (DFT) is notorious for the absence of gradient corrections to the two-dimensional (2D) Thomas-Fermi kinetic-energy functional; it is widely accepted that the 2D analog of the 3D von Weizs\"acker correction…

Two families of strongly non-Gaussian random matrix ensembles (RME) are considered. They are statistically equivalent to a one-dimensional plasma of particles interacting logarithmically and confined by the potential that has the long-range…

We demonstrate the convergence of the characteristic polynomial of several random matrix ensembles to a limiting universal function, at the microscopic scale. The random matrix ensembles we treat are classical compact groups and the…

There are several physically motivated density matrix functionals in the literature, built from the knowledge of the natural orbitals and the occupation numbers of the one-body reduced density matrix. With the help of the equivalent…

Time-dependent density functional theory (TDDFT) is a standard approach for calculating optical excitations of molecules and solids, while ensemble DFT (EDFT) is a promising alternative under development. We introduce ensemble TDDFT…

We consider a system of particles interacting via a purely repulsive, soft-core potential recently introduced to model effective pair interactions between dendrimers, which is expected to lead to the formation of crystals with multiple…

The Pauli exclusion principle requires the spectrum of the occupation numbers of the one-electron reduced density matrix (1-RDM) to be bounded by one and zero. However, for a 1-RDM from a wave function, there exist additional conditions on…

Normal matrices, or matrices which commute with their adjoints, are of fundamental importance in pure and applied mathematics. In this paper, we study a natural functional on the space of square complex matrices whose global minimizers are…

Deep-learning density functional theory (DFT) shows great promise to significantly accelerate material discovery and potentially revolutionize materials research. However, current research in this field primarily relies on data-driven…

Aspects of Density Functional Resonance Theory (DFRT) [Phys. Rev. Lett. \textbf{107}, 163002 (2011)], a recently developed complex-scaled version of ground-state Density Functional Theory (DFT), are studied in detail. The asymptotic…

We give new characterizations for the class of uniformly dense matroids and study applications of these characterizations to graphic and real representable matroids. We show that a matroid is uniformly dense if and only if its base polytope…

We provide a simple analytic relation which connects the density operator of the radiation field with the number probabilities. The problem of experimentally "sampling" a general matrix elements is studied, and the deleterious effects of…

The key features of density-functional theory (DFT) within a minimalistic implementation of quantum electrodynamics are demonstrated, thus allowing to study elementary properties of quantum-electrodynamical density-functional theory…