Related papers: Wavefunctions for large electronic systems
We develop a new density functional theory (DFT) and formalism for correlated electron systems by taking as reference an interacting electron system that has a ground state wavefunction which obeys exactly the Gutzwiller approximation for…
The charge density and pair correlation function of three interacting electrons confined within a two-dimensional disc-like hard wall quantum dot are calculated by full numerical diagonalization of the Hamiltonian. The formation of a…
Quantum mechanical many-electron calculations can predict properties of atoms, molecules and even complex materials. The employed computational methods play a quintessential role in many scientifically and technologically relevant research…
A new class of analytic wave functions is derived for two dimensional N-electron (2 <= N < infinity) systems in high magnetic fields. These functions are constructed through breaking (at the Hartree-Fock level) and subsequent restoration…
We demonstrate the existence of different density-density functionals designed to retain selected properties of the many-body ground state in a non-interacting solution starting from the standard density functional theory ground state. We…
A multiresolution analysis for a Hilbert space realizes the Hilbert space as the direct limit of an increasing sequence of closed subspaces. In a previous paper, we showed how, conversely, direct limits could be used to construct Hilbert…
We combine Maxwell's equations with Eulers's equation, related to a velocity field of an immaterial fluid, where the density of mass is replaced by a charge density. We come out with a differential system able to describe a relevant…
We prove that the electron density function of a real physical system can be uniquely determined by its values on any finite subsystem. This establishes the existence of a rigorous density-functional theory for any open electronic system.…
Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman-von Neumann-Sudarshan prescription for classical mechanics on Hilbert spaces {\em sans} the…
Density functional theory (DFT) provides a theoretical framework for efficient and fairly accurate calculations of the electronic structure of molecules and crystals. The main features of density functional theory are described and DFT…
We develop an ensemble density functional theory for the fractional quantum Hall effect using a local density approximation. Model calculations for edge reconstructions of a spin-polarized quantum dot give results in good agreement with…
A linear algebraic method named the shifted conjugate-orthogonal-conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green's function and the…
Electronic structure codes usually allow to calculate the work function as a part of the theoretical description of surfaces and processes such as adsorption thereon. This requires a proper calculation of the electrostatic potential in all…
We revisit the three-body problem in quantum mechanics in two and three dimensions, generating both exact eigenvalues and eigenvectors of the Hamiltonian and a series of approximate solutions as calculated with a variety of different…
The electronic band structures of two-dimensional materials are significantly different from those of their bulk counterparts, due to quantum confinement and strong modifications of electronic screening. An accurate determination of…
Understanding of bonding is key to modelling materials and predicting properties thereof. A widely adopted indicator of bonds and atomic shells is the electron localization function (ELF). The building blocks of the ELF are also used in the…
Electronic correlation is a fundamental topic in many-electron systems. To characterize this correlation, one may introduce the concept of exchange-correlation hole. In this paper, we first briefly revisit its definition and relation to…
We study the wave analog of the Liouville equation and the constant mean curvature equations in 2 space dimensions, which are energy critical. We exhibit a blow-up criteria for the former using tools from conformal geometry, and we exhibit…
We suggest to include the density of electron charge explicitly in the electron potential of density functional theory, rather than implicitly via exchange-correlation functionals. The advantages of the approach are conceptual and…
We present an efficient \textit{ab initio} method for calculating the electronic structure and total energy of strongly correlated electron systems. The method extends the traditional Gutzwiller approximation for one-particle operators to…