Related papers: Geometrical Perspective on Spin-Lattice Density-Fu…
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 study the mapping between time-dependent densities and potentials for noninteracting electronic systems on lattices. As discovered recently by Baer [J. Chem. Phys. 128, 044103 (2008)], there exist well-behaved time-dependent density…
An interacting lattice model describing the subspace spanned by a set of strongly-correlated bands is rigorously coupled to density functional theory to enable ab initio calculations of geometric and topological material properties. The…
A rigorous derivation of the density functional in the Hohenberg-Kohn theory is presented. With no assumption regarding the magnitude of the electric coupling constant $e^2$ (or correlation), this work provides a firm basis for…
An approximate analytical scheme of the dynamical mean field theory (DMFT) is developed for the description of the electron (ion) lattice systems with Hubbard correlations within the asymmetric Hubbard model where the chemical potentials…
A real-space formalism for density-functional perturbation theory (DFPT) is derived and applied for the computation of harmonic vibrational properties in molecules and solids. The practical implementation using numeric atom-centered…
We explore a variety of unsolved problems in density functional theory, where mathematicians might prove useful. We give the background and context of the different problems, and why progress toward resolving them would help those doing…
The magnetic properties of a system of coexisting localized spins and conduction electrons are investigated within an extended version of the one dimensional Kondo lattice model in which effects stemming from the electron-lattice and…
Relativistic deformed kinematics leads to a loss of the absolute locality of interactions. In previous studies, some models of noncommutative spacetimes in a two-particle system that implements locality were considered. In this work, we…
Accurate description of deformed atomic nuclei by the orbital-free density functional theory has been a longstanding textbook challenge, due to the difficulty in accounting for the intricate quantum shell effects that are present in such…
Time-dependent density functional theory, proposed recently in the context of atomic diffusion and non-equilibrium processes in solids, is tested against Monte Carlo simulation. In order to assess the basic approximation of that theory, the…
A generalization of the Density Functional Theory is proposed. The theory developed leads to single-particle equations of motion with a quasi-local mean-field operator, which contains a quasi-particle position-dependent effective mass and a…
The rotating nuclei represent one of most interesting subjects for theoretical and experimental studies. They open a new dimension of nuclear landscape, namely, spin direction. Contrary to the majority of nuclear systems, their properties…
Understanding the quantum dynamics of spin defects and their coherence properties requires accurate modeling of spin-spin interaction in solids and molecules, for example by using spin Hamiltonians with parameters obtained from…
Weakly interacting Fermi gases exhibit rich collective dynamics in spin-dependent potentials, arising from correlations between spin degrees of freedom and conserved single atom energies, offering broad prospects for simulating many-body…
Spin fluctuations have a substantial influence on the electron and lattice behaviors in magnetic materials, which, however, is difficult to be tracked properly by prevalent first-principles methods. We propose a versatile self-adaptive…
The formalism of Kohn and Sham uses a specific (model) hamiltonian which highly simplifies the many-electron problem to that of noninteracting fermions. The theorem of Hohenberg and Kohn tells us that, for a given ground state density, this…
Coordinate scaling of each spin density separately is considered in spin density functional theory. A virial theorem relates the spin-scaled correlation energy to the spin-scaled correlation potentials. An adiabatic connection formula…
The spectroscopic quality of covariant density functional theory has been accessed by analyzing the accuracy and theoretical uncertainties in the description of spectroscopic observables. Such analysis is first presented for the energies of…
In this chapter we first review the Levy-Lieb functional, which gives the lowest kinetic and interaction energy that can be reached with all possible quantum states having a given density. We discuss two possible convex generalizations of…