Related papers: Gradient corrections to the local density approxim…
The local density of states (LDOS) in finite quantum wires is calculated as a function of discrete energies and position along the wire. By using a combination of numerical density matrix renormalization group (DMRG) calculations and…
We study the Mott insulating phase of the one-dimensional Hubbard model using a local-density approximation (LDA) that is based on the Bethe Ansatz (BA). Unlike conventional functionals, the BA-LDA has an explicit derivative discontinuity.…
We derive and analyze the coupled equations of quadratic approximation of the Bogoliubov model for a weakly interacting Bose gas. The first equation determines the condensate density as a variational parameter and ensures the minimum of the…
As one of the most popular linear subspace learning methods, the Linear Discriminant Analysis (LDA) method has been widely studied in machine learning community and applied to many scientific applications. Traditional LDA minimizes the…
We consider the K-body local correlations in the (repulsive) 1D Bose gas for general K, both at finite size and in the thermodynamic limit. Concerning the latter we develop a multiple integral formula which applies for arbitrary states of…
Motivated by high-accuracy scanning tunneling spectroscopy measurements on disordered two-dimensional electron gases in strong magnetic field, we present an exact solution for the local density of states (LDoS) of electrons moving in an…
We propose a new method to describe the interacting bose gas at zero temperature. We use the decomposition of the logarithm of the wave function into the irreducible $n$-point functions. We argue that in the low density limit this expansion…
The Lieb-Liniger equation of state accurately describes the zero-temperature universal properties of a dilute one-dimensional Bose gas in terms of the s-wave scattering length. For weakly-interacting bosons we derive non-universal…
Power law suppression of local electronic tunneling density of states (TDOS) in the zero-energy limit is a hallmark of Luttinger liquid (LL) phase of the interacting 1-D electron system. We present a theoretical model which hosts LL state…
We construct a Laplacian-level meta-generalized gradient approximation (meta-GGA) for the non-interacting (Kohn-Sham orbital) positive kinetic energy density $\tau$ of an electronic ground state of density $n$. This meta-GGA is designed to…
Data assimilation (DA) integrates observations with model forecasts to produce optimized atmospheric states, whose physical consistency is critical for stable weather forecasting and reliable climate research. Traditional Bayesian DA…
The well-known results concerning a dilute Bose gas with the short-range repulsive interaction should be reconsidered due to a thermodynamic inconsistency of the method being basic to much of the present understanding of this subject. The…
In this paper we revisit a two-level discretization based on the Localized Orthogonal Decomposition (LOD). It was originally proposed in [P.Henning, A.M{\aa}lqvist, D.Peterseim. SIAM J. Numer. Anal.52-4:1525-1550, 2014] to compute ground…
For closed-shell systems, the local density approximation (LDA) and the LYP, BLYP, and B3LYP functionals are shown to be compatible with reference-state one-particle density-matrix theory, where this recently introduced formalism is based…
Recent experimental and theoretical work has indicated conditions in which a trapped, low-density Bose gas ought to behave like the 1D delta-function Bose gas solved by Lieb and Liniger. Up to now the theoretical arguments have been based…
We discuss the application of the density functional theory in the local density approximation (LDA) near a ferromagnetic quantum critical point. The LDA fails to describe the critical fluctuations in this regime. This provides a…
We consider several models of interacting bosons in a one dimensional lattice. Some of them are not integrable like the Bose-Hubbard others are integrable. At low density all of these models can be described by the Bose gas with delta…
DFT-1/2 is an efficient band gap rectification method for density functional theory (DFT) under local density approximation (LDA) or generalized gradient approximation. It was suggested that non-self-consistent DFT-1/2 should be used for…
The uniform electron gas and the hydrogen atom play fundamental roles in condensed matter physics and quantum chemistry. The former has an infinite number of electrons uniformly distributed over the neutralizing positively-charged…
We study the ground state of a system of Bose hard-spheres trapped in an isotropic harmonic potential to investigate the effect of the interatomic correlations and the accuracy of the Gross-Pitaevskii equation. We compare a local density…