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A curious behavior of electron correlation energy is explored. Namely, the correlation energy is the energy that tends to drive the system toward that of the uniform electron gas. As such, the energy assumes its maximum value when a…
We consider a class of nonconvex energy functionals that lies in the framework of the peridynamics model of continuum mechanics. The energy densities are functions of a nonlocal strain that describes deformation based on pairwise…
We introduce a large class of scalar-tensor models with interactions containing the second derivatives of the scalar field but not leading to additional degrees of freedom. These models exhibit peculiar features, such as an essential mixing…
The non-equilibrium densities of nonlocal mass-energy are self-governed by kinetic stresses toward quasi-equilibrium sub-configurations. System energy integral of continuous matter-extension coordinates its adaptive densities on each…
We construct a configurational entropy measure in functional space. We apply it to several nonlinear scalar field models featuring solutions with spatially-localized energy, including solitons and bounces in one spatial dimension, and…
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…
A Kohn-Sham density-functional energy expression is derived for any (ground or excited) state within a given many-electron ensemble along with the stationarity condition it fulfills with respect to the ensemble density, thus giving access…
The canonical energy-momentum tensor is often considered as a purely academic object because of its gauge dependence. However, it has recently been realized that canonical quantities can in fact be defined in a gauge-invariant way provided…
Phase space reflection operators lie at the core of the Wigner-Weyl representation of density operators and observables. The role of the corresponding classical reflections is known in the construction of semiclassical approximations to…
Scale-space energy density function, $E(\mathbf{x}, \mathbf{r})$, is defined as the derivative of the two-point velocity correlation. The function E describes the turbulent kinetic energy density of scale r at a location x and can be…
While ab initio many-body techniques have been able to successfully describe the properties of light and intermediate mass nuclei based on chiral effective field theory interactions, neutron-rich nuclei still remain out of reach for these…
We show that the stress-energy tensor has additional terms with respect to the ideal form in states of global thermodynamic equilibrium in flat spacetime with non-vanishing acceleration and vorticity. These corrections are of quantum origin…
Semilocal density functionals for the exchange-correlation energy are needed for large electronic systems. The Tao-Perdew-Staroverov-Scuseria (TPSS) meta-generalized gradient approximation (meta-GGA) is semilocal and usefully accurate, but…
Following a recent work [Gal, Phys. Rev. A 64, 062503 (2001)], a simple derivation of the density-functional correction of the Hartree-Fock equations, the Hartree-Fock-Kohn-Sham equations, is presented, completing an integrated view of…
A widely used approximation to the exchange-correlation functional in density functional theory is the local density approximation (LDA), typically derived from the properties of the homogeneous electron gas (HEG). We previously introduced…
Using an end-to-end differentiable implementation of the Kohn-Sham self-consistent field equations, we obtain an accurate neural network-based exchange and correlation (XC) functional of the electronic density. The functional is optimized…
We extend the Vanderbilt ultrasoft pseudopotential scheme by adding kinetic energy density terms, in order to use meta-GGA exchange potentials, such as the Becke-Johnson or Tran-Blaha potentials, in the planewave-pseudopotential…
Energy density functionals (EDFs) have been used extensively with great success to calculate properties of nuclei and to predict the equation of state (EOS) of dense nuclear matter. Besides non-relativistic EDFs, mostly of the Skyrme or…
Brueckner orbitals, and the density of the Brueckner reference-state, are shown to satify the same cusp condition -- involving the nuclear charges -- as natural- and Hartree--Fock-orbitals. Using the cusp condition, the density of a…
The Airy gas model of the edge electron gas is used to construct an exchange-energy functional which is an alternative to those obtained in the local density and generalized gradient approximations. Test calculations for rare gas atoms,…