Related papers: Accurate ground-state energies of Wigner crystals …
The quantum-classical crossover from the Fermi liquid towards the Wigner solid is numerically revisited, considering small square lattice models where electrons interact via a Coulomb $U/r$ potential. The studies of models without disorder…
A Wigner crystal structure of the electronic ground state is induced by strong Coulomb interactions at low temperature in clean or disordered two-dimensional (2d) samples. For fermions on a mesoscopic disordered 2d lattice, being closed to…
We provide the first counterexample showing that the ground state energy of electrons in an external Coulomb potential is not always a convex function of the number of electrons. This convexity has been conjectured for decades and plays an…
Wigner crystals are prime candidates for the realization of regular electron lattices under minimal requirements on external control and electronics. However, several technical challenges have prevented their detailed experimental…
The method of images is used to calculate the Casimir energy in Euclidean space with Dirichlet boundary conditions for two planar models, namely: i. the non-relativistic Landau problem for a charged particle of mass m for which -…
The one-dimensional quantum spin-1/2 model with nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interaction is considered. The Hamiltonian is first bosonized by using the linear spin wave approximation, and then…
In an external constant magnetic field, so strong that the electron Larmour length is much shorter than its Compton length, we consider the modification of the Coulomb potential of a point charge owing to the vacuum polarization. We…
The purpose of this paper is to derive sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, and, in particular, to derive relativistic Scott correction term and also Dirac, Schwinger…
This work concerns \emph{ab initio} calculations of the complete potential energy curve and spectroscopic constants for the ground state $X^1\Sigma_g^+$ of the beryllium dimer, Be$_2$. High accuracy and reliability of the results is one of…
Low-disorder two-dimensional electron systems in the presence of a strong, perpendicular magnetic field terminate at very small Landau level filling factors in a Wigner crystal (WC), where the electrons form an ordered array to minimize the…
We extend our previous result on the nonlinear Klein-Gordon equation to the nonlinear Schrodinger equation with the focusing cubic nonlinearity in three dimensions, for radial data of energy at most slightly above that of the ground state.…
We establish an asymptotic formula for the ground-state energy of the spherical pure $(p,q)$-spin glass model for $p,q\ge 97$. We achieve this through understanding the concentration of the complexity of critical points with values within a…
We study a class of exactly solvable models for strongly correlated electrons, defined on a set of N cells, and with infinite on-site repulsion on part of the sites of each cell. For 2N or more electrons the exact ground state is known. We…
Ground-state energies of the one- and two-electron uranium dimers are calculated for internuclear distances in the range D=40--1000 fm and compared with the previous calculations. The generalization of the dual-kinetic-balance approach for…
We compute the ground state energy of atoms and quantum dots with a large number N of electrons. Both systems are described by a non-relativistic Hamiltonian of electrons in a d-dimensional space. The electrons interact via the Coulomb…
We make a comparison between the energy levels of the hydrogen atom, calculated by using standard methods, and that by using a modified Coulomb potential due to the interaction between the magnetic moments of the proton and electron. In…
A floating Wigner crystal differs from the standard one by a spatial averaging over positions of the Wigner-crystal lattice. It has the same internal structure as the fixed crystal, but contrary to it, takes into account rotational and/or…
We present a fully quantum-mechanical study of the energy-momentum dispersion of running waves, spin-conserving neutral excitations, and spin-reversal neutral excitations in a spin-polarized two-dimensional Wigner crystal (WC). Our results…
The spectral properties of up to four interacting electrons confined within a quasi one--dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground state energy is…
When two-dimensional electrons are subjected to a very strong magnetic field, they are believed to form a triangular Wigner crystal. We demonstrate that, in the entire crystal phase, this crystal is very well represented by a…