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We consider density functionals for exchange and correlation energies in two-dimensional systems. The functionals are constructed by making use of exact constraints for the angular averages of the corresponding exchange and correlation…
We revisit the statistical mechanics of charge fluctuations in capacitors. In constant-potential classical molecular simulations, the atomic charge of electrode atoms are treated as additional degrees of freedom which evolve in time so as…
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…
A density-functional theory is developed based on the Maxwell--Schr\"odinger equation with an internal magnetic field in addition to the external electromagnetic potentials. The basic variables of this theory are the electron density and…
We consider interacting Fermi systems close to the unitary regime and compute the corrections to the energy density that are due to a large scattering length and a small effective range. Our approach exploits the universality of the density…
The organization of water molecules and ions between charged mineral surfaces determines the stability of colloidal suspensions and the strength of phase-separated particulate gels. In this article we assemble a density functional that…
In this paper, we study some properties such as the monotonicity, logarithmically complete monotonicity, logarithmic convexity, and geometric convexity, of the combinations of gamma function and power function. The results we obtain…
We introduce an orbital free electron density functional approximation based on alchemical perturbation theory. Given convergent perturbations of a suitable reference system, the accuracy of popular self-consistent Kohn-Sham density…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
Based on recent progress on fermionic exchange symmetry we propose a way to develop new functionals for reduced density matrix functional theory. For some settings with an odd number of electrons, by assuming saturation of the inequalities…
Equilibrium polyethylene crystal structure, cohesive energy, and elastic constants are calculated by density-functional theory applied with a recently proposed density functional (vdW-DF) for general geometries [Phys. Rev. Lett. 92, 246401…
We present a method aimed at sampling charge density fluctuations in Coulomb systems. The derivation follows from a functional integral representation of the partition function in terms of charge density fluctuations. Starting from the…
A simple comparison between the exact and approximate correlation components U of the electron-electron repulsion energy of several states of few-electron harmonium atoms with varying confinement strengths provides a superior validation…
We show a general phenomenon of the constrained functional value for densities satisfying general convexity conditions, which generalizes the observation in Bobkov and Madiman (2011) that the entropy per coordinate in a log-concave random…
The Debye-H\" uckel formula for ionic activity coefficients is extended for concentrated solutions by solving a simple model of many-body Coulomb correlations and adding the Born solvation energy. Given the bulk permittivity, our formula is…
Using the complex Langevin sampling strategy, field theoretic simulations are performed to study the equilibrium phase behavior and structure of symmetric polycation-polyanion mixtures without salt in good solvents. Static structure factors…
A theoretical description for the radial density profile of a finite number of identical charged particles confined in a harmonic trap is developed for application over a wide range of Coulomb coupling (or, equivalently, temperatures) and…
Classical density-functional theory provides an efficient alternative to molecular dynamics simulations for understanding the equilibrium properties of inhomogeneous fluids. However, application of density-functional theory to multi-site…
We show that certain free energy functionals that are not convex with respect to the usual convex structure on their domain of definition, are strictly convex in the sense of displacement convexity under a natural change of variables. We…
We develop a double mean-field theory for charged macrogels immersed in electrolyte solutions in the spirit of the cell model approach. We first demonstrate that the equilibrium sampling of a single explicit coarse-grained charged polymer…