相关论文: Symmetric Density Functionals

Density functional theory is usually formulated in terms of the density in configuration space. Functionals of the momentum-space density have also been studied, and yet other densities could be considered. We offer a unified view from a…

A method for interpreting discontinuities of the twist potential of vacuum stationary axisymmetric solutions of Einstein's equations is introduced. Surface densities for the angular momentum of the source can be constructed after solving a…

Recently, Theophilou (J. Chem.Phys {\bf 149} 074104 (2018)) showed that a set of spherically symmetric densities determines uniquely the external potential in molecules and solids. Here, spherically symmetric Kohn-Sham-like equations are…

A method to separate a Slater determinant wave function with a two-center neck structure into spatially localized subsystems is proposed, and its potential applications are presented. An orthonormal set of spatially localized…

Using a hydrogen molecule as a test system we demonstrate how to compute the effective potential according to the formalism of the new density functional theory (DFT), in which the basic variable is the set of spherically averaged densities…

It is shown that, contrary to widely held beliefs, the potentials of spin-density-functional theory (SDFT) are not unique functionals of the spin densities. Explicit examples of distinct sets of potentials with the same ground-state…

A method is presented for finding anisotropic distribution functions for stellar systems with known, spherically symmetric, densities, which depends only on the two classical integrals of the energy and the magnitude of the angular…

The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…

A generating coordinate is introduced into the exchange-correlation functional of density-functional theory (DFT). The many-body wave function is represented as a superposition of Kohn-Sham (KS) Slater determinants arising from different…

We derive a general relation between correlators of density of states fluctuations and density response functions. It applies equally to quantum chaotic systems of pure symmetry (unitary, orthogonal, and symplectic) as well as to the…

Density-functional theory is used to study the electronic structure of quantum dots in a magnetic field. New series of magic numbers are found for the total angular momentum of electrons. The empirical formula for the plateau width is…

Potential functional approximations are an intriguing alternative to density functional approximations. The potential functional that is dual to the Lieb density functional is defined and properties given. The relationship between…

We show how every bound state of a finite system of identical fermions, whether a ground state or an excited one, defines a density functional. Degeneracies created by a symmetry group can be trivially lifted by a pseudo-Zeeman effect. When…

Gleason's theorem asserts the equivalence of von Neumann's density operator formalism of quantum mechanics and frame functions, which are functions on the pure states that sum to 1 on any orthonormal basis of Hilbert space of dimension at…

A variant of the basic Skyrme-Hartree-Fock (SHF) functional is considered dealing with a new form of density dependence. It employs only integer powers and thus will allow a more sound basis for projection schemes (particle number, angular…

In quantum mechanics, spatial wavefunctions describe distributions of a particle's position or momentum, but not of angular momentum $j$. In contrast, here we show that a spatial wavefunction, $j_m (\phi,\theta,\chi)=~e^{i m \phi} \delta…

The second-quantized form of the Laughlin states for the fractional quantum Hall effect is discussed by decomposing the Laughlin wavefunctions into the $N$-particle Slater basis. A general formula is given for the expansion coefficients in…

In this lecture we deal with the construction of surface densities for the angular momentum of the sources of asymptotically flat vacuum stationary axisymmetric spacetimes. These sources arise from the discontinuities of the twist…

One and two photon wave functions are derived by projecting the quantum state vector onto simultaneous eigenvectors of the number operator and a recently constructed photon position operator [Phys. Rev A 59, 954 (1999)] that couples spin…

We present a machine learning algorithm for the prediction of molecule properties inspired by ideas from density functional theory. Using Gaussian-type orbital functions, we create surrogate electronic densities of the molecule from which…