Related papers: Thermodynamic Limits of Electronic Systems
We proposed a formally exact, probabilistic method to assess the validity of the Thomas-Fermi potential for three-dimensional condensed matter systems where electron dynamics is constrained to the Fermi surface. Our method, which relies on…
In this paper, we study finite dimensional approximations of Kohn-Sham models, which are widely used in electronic structure calculations. We prove the convergence of the finite dimensional approximations and derive the a priori error…
We consider a tight binding model for localised crystalline defects with electrons in the canonical ensemble (finite electronic temperature) and nuclei positions relaxed according to the Born--Oppenheimer approximation. We prove that the…
One of the goals in the development of large scale electronic structure methods is to perform calculations explicitly for a localised region of a system, while still taking into account the rest of the system outside of this region. An…
Many-electron systems at substantial finite temperatures and densities present a major challenge to density functional theory. Very little is known about the free-energy behavior over the temperature range of interest, for example, in the…
We study Density Functional Theory models for systems which are translationally invariant in some directions, such as a homogeneous 2-d slab in the 3-d space. We show how the different terms of the energy are modified and we derive reduced…
We derive a self-consistent local variant of the Thomas-Fermi approximation for (quasi-)two-dimensional (2D) systems by localizing the Hartree term. The scheme results in an explicit orbital-free representation of the electron density and…
We present two recent works on the thermodynamic limit of quantum Coulomb systems, in which we provided a general method allowing to show the existence of the limit for many different models.
In this paper we study a class of physical systems that combine a finite number of mechanical and thermodynamic observables. We call them finite dimensional thermo-mechanical systems. We introduce these systems by means of simple examples.…
The Kohn-Sham scheme of density functional theory is one of the most widely used methods to solve electronic structure problems for a vast variety of atomistic systems across different scientific fields. While the method is fast relative to…
The confinement mechanism of electrons in gated circular quantum dots is studied in a sequence of models, from self-consistent 3D Hartree calculations to the semiclassical model of Shikin et al. Separation of the vertical from transverse…
Linear-scaling electronic structure methods based on the calculation of moments of the underlying electronic Hamiltonian offer a computationally efficient and numerically robust scheme to drive large-scale atomistic simulations, in which…
This article is part-I of a review of density-functional theory (DFT) that is the most widely used method for calculating electronic structure of materials. The accuracy and ease of numerical implementation of DFT methods has resulted in…
In this work we solve thermo-hydrodynamical equations considering a two dimensional electron system in the integer quantum Hall regime, to calculate the spatial distribution of the local electron temperature. We start from the…
Lattice parameter, electronic structure, mechanical and thermodynamic properties of ThN are systematically studied using the projector-augmented-wave method and the generalized gradient approximation based on the density functional theory.…
In this work we describe, compile and generalize a set of tools that can be used to analyse the electronic properties (distribution of states, nature of states, ...) of one-dimensional disordered compositions of potentials. In particular,…
The formalism developed in the first paper of the series [arXiv:0901.1060] is applied to two thermodynamic systems: (i) of three global observables (the energy, the total electron number and the spin number), (ii) of one global observable…
By introducing the self-energy density functionals for the dissipative interactions between the reduced system and its environment, we develop a time-dependent density-functional theory formalism based on an equation of motion for the…
The Thomas-Fermi (TF) approximation for the static dielectric constant of a three-dimensional electron liquid can be derived from minimizing the TF local-density approximation for the kinetic-energy functional. Here we show that this…
Limiting structure of thermodynamic functions of gaseous plasmas is under consideration in the limit of low temperature and density. The remarkable tendency, that was claimed previously [High Temp. 19, 799 (1981)], is carried to extreme. In…