Related papers: Lower Bounds on the Exchange-Correlation Energy in…
For the two-dimensional electron gas, the exact high-density limit of the correlation energy is evaluated here numerically for all values of the spin polarization. The result is spin-resolved into $\uparrow\uparrow$, $\uparrow\downarrow$,…
Relationships between the coupling constant and the binding energy of threshold bound states are obtained in a simple manner from an iterative algorithm for solving the eigenvalue problem. The absence of threshold bound states in higher…
We consider a system of $N\gg 1$ interacting fermionic particles in three dimensions, confined in a periodic box of volume $1$, in the mean-field scaling. We assume that the interaction potential is bounded and small enough. We prove upper…
Low-lying energy levels of two interacting electrons confined in a two-dimensional parabolic quantum dot in the presence of an external magnetic field have been revised within the frame of a novel model. The present formalism, which gives…
Recent progress in the formulation of a fully dynamical local approximation to time-dependent Density Functional Theory appeals to the longitudinal and transverse components of the exchange and correlation kernel in the linear…
The dynamical response theory is used to obtain an analytical expression for the exchange energy of a quantum wire for arbitrary polarization and width. It reproduces the known form of exchange energy for 1D electron gas in the limit of…
We investigate the effect of electron-electron interactions on the conductance of quasi one-dimensional systems without potential scattering. For a finite temperature or system length, the short-range interaction is not renormalized to 0,…
We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such…
A theory is developed for the evolution of the non-equilibrium distribution of quasiparticles when the scattering rate decreases due to particle collisions. We propose a "modified one-collision approximation" which is most effective for…
The momentum space zero-range model is used to investigate universal properties of three interacting particles confined to two dimensions. The pertinent equations are first formulated for a system of two identical and one distinct particle…
The transport properties of interacting electrons for which the spin degree of freedom is taken into account are numerically studied for small two dimensional diffusive clusters. On-site electron-electron interactions tend to delocalize the…
We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…
Nonuniversal effects due to leading effective-range corrections are computed for the ground-state energy of the weakly-coupled repulsive Bose gas in two spatial dimensions. Using an effective field theory of contact interactions, these…
Entanglement is not only the resource that fuels many quantum technologies but also plays a key role for some of the most profound open questions of fundamental physics. Experiments controlling quantum systems at the single quantum level…
We calculate the dynamic effective electron-electron interaction potential for a low density disordered two-dimensional electron gas. The disordered response function is used to calculate the effective potential where the scattering rate is…
A simple formula for correlation energy $E_c$ of the $\pi$ electron systems is obtained under an approximation for the electron-electron interactions. This formula is related directly to square of the bond order matrix and the…
Entanglement entropies have revealed, in the last years, to be a powerful tool to extract information about the physics of condensed-matter systems. In the first part of this thesis, we show how to extract essential details about the…
Radial, angular and total correlation energies are calculated for four two-electron systems with atomic numbers Z=0-3 confined within an impenetrable sphere of radius R. We report accurate results for the non-relativistic, restricted…
We consider one-dimensional tubes containing bosonic polar molecules. The long-range dipole-dipole interactions act both within a single tube and between different tubes. We consider arbitrary values of the externally aligned dipole moments…
We study non-linear adiabatic connection paths in density-functional theory using modified electron-electron interactions that perform a long-range/short-range separation of the Coulomb interaction. These adiabatic connections allows to…