Related papers: A note about the ground state of the hydrogen mole…
We present a new method for calculating ground state properties of quantum dots in high magnetic fields. It takes into account the equilibrium positions of electrons in a Wigner cluster to minimize the interaction energy in the high field…
Within the framework of a one-dimensional model of interacting electrons, the ground state of an electron liquid is studied. Using the exact solution of the model, the ground state phase diagram and zero-energy Majorana edge functions in a…
We present the results of a systematic search for molecular hydrogen (H2) in low redshift ($ 0.05 \lesssim z \lesssim 0.7$) DLAs and sub-DLAs with $N(HI) \gtrsim 10^{19.0}$ cm$^{-2}$, in the archival HST/COS spectra. Our core sample is…
Exact density functionals for the exchange and correlation energies are approximated in practical calculations for the ground-state electronic structure of a many-electron system. An important exact constraint for the construction of…
The exact ground state of four electrons in an arbitrary large two leg Hubbard ladder is deduced from nine analytic and explicit linear equations. The used procedure is described, and the properties of the ground state are analyzed. The…
In this work we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the…
The ground state energy of hydrogen molecular ion H2+ confined by a hard prolate spheroidal cavity is calculated. The case in which the nuclear positions are clamped at the foci is considered. Our calculations are based on using the…
Although the existence of quasi-bound rotational levels of the $X^+ \ ^2\Sigma_g^+$ ground state of H$_2^+$ has been predicted a long time ago, these states have never been observed. Calculated positions and widths of quasi-bound rotational…
The electronic structure of Ce2 is studied in a valence bond model with two 4f electrons localized at two cerium sites. It is shown that the low-lying energy spectrum of the simplest cerium chemical bond is determined by peculiarities of…
The Pade approximant technique and the variational Monte Carlo method are applied to determine the ground-state energy of a finite number of charged bosons in two dimensions confined by a parabolic trap. The particles interact repulsively…
Molecular hydrogen is a benchmark system for bound state quantum calculation and tests of quantum electrodynamical effects. While spectroscopic measurements on the stable species have progressively improved over the years, high resolution…
Coupled semiconductor quantum dots form artificial molecules where relevant energy scales controlling the interacting ground state can be easily tuned. By applying an external magnetic field it is possible to drive the system from a weak to…
The weak coupling asymptotics, to order $(c/\rho)^2$, of the ground state energy of the delta-function Bose gasmis derived. Here $2c\ge 0$ is the delta-function potential amplitude and $\rho$ the density of the gas in the thermodynamic…
Ultrashort non-resonant electromagnetic pulses applied to effective one-electron systems may operate on the electronic state as a position or momentum translation operator. As derived here, extension to many-body correlated systems exposes…
The variational argument is presented to establish the attainability of homogeneity of degree one in the number of particles for any functional $F[n, f]$ that depends on both the state variable $f$ and the particle count $n$. Euler's…
In this chapter, we provide a review of ground-state Kohn-Sham density-functional theory of electronic systems and some of its extensions, we present exact expressions and constraints for the exchange and correlation density functionals,…
The hyperspherical harmonics (HH) provide a complete basis for the expansion of atomic wave functions, but even for two particles the number of harmonics for a given order is not trivial and, as the number of electrons increases, this…
The rotational sublevels of the key (000) and (010) vibrational states of the H2S molecule were modeled with an accuracy close to experimental uncertainty using the generating function and Euler approaches. The predictive ability of the…
We substantiate the need for account of the proper electromagnetic field of the electron in the canonical problem of hydrogen in relativistic quantum mechanics. From mathematical viewpoint, the goal is equivalent to determination of the…
We verify Bogoliubov's approximation for translation invariant Bose gases in the mean field regime, i.e. we prove that the ground state energy $E_N$ is given by $E_N=Ne_\mathrm{H}+\inf \sigma\left(\mathbb{H}\right)+o_{N\rightarrow…