Related papers: A step toward density benchmarking -- the energy-r…

In recent years impressive progress has been made in the development of highly accurate energy density functionals, which allow to treat medium-heavy nuclei. In this approach one tries to describe not only the ground state but also the…

Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and…

Density functional theory (DFT) is an incredible success story. The low computational cost, combined with useful (but not yet chemical) accuracy, has made DFT a standard technique in most branches of chemistry and materials science.…

Mean field theory models of percolation on networks provide analytic estimates of network robustness under node or edge removal. We introduce a new mean field theory model based on generating functions that includes information about the…

The motion of an electron in an image field and a blocking electric field is considered in semiclassical approximation. An exact analytical expression is found for the density of the energy spectrum of states. The dependence of spectral…

We propose a new molecular simulation framework that combines the transferability, robustness and chemical flexibility of an ab initio method with the accuracy and efficiency of a machine learned force field. The key to achieve this mix is…

This chapter introduces thermal density functional theory, starting from the ground-state theory and assuming a background in quantum mechanics and statistical mechanics. We review the foundations of density functional theory (DFT) by…

I present a review on non relativistic effective energy--density functionals (EDFs). An introductory part is dedicated to traditional phenomenological functionals employed for mean--field--type applications and to several extensions and…

Nuclear density functional theory is the prevalent theoretical framework for accurately describing nuclear properties at the scale of the entire chart of nuclides. Given an energy functional and a many-body scheme (e.g., single- or…

Density estimation is a central primitive in probabilistic modeling, yet continuous, discrete, and mixed-variable domains are often treated by separate objectives, limiting the ability to exploit a common statistical structure across data…

Density functional theory is the workhorse of modern electronic structure calculations, with wide-ranging applications in chemistry, physics, materials science, and machine learning. At its heart lies the exchange-correlation functional, a…

Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems…

Rich out of equilibrium collective dynamics of strongly interacting large assemblies emerge in many areas of science. Some intriguing and not fully understood examples are the glassy arrest in atomic, molecular or colloidal systems,…

The effectiveness and performance of artificial neural networks, particularly for visual tasks, depends in crucial ways on the receptive field of neurons. The receptive field itself depends on the interplay between several architectural…

Approximate functionals used in practical density functional theory (DFT) deviate from the piecewise linear behavior of the exact functional for fractional charges. This deviation causes excess charge delocalization, which leads to…

In this paper we focus on the linear functionals defining an approximate version of the gradient of a function. These functionals are often used when dealing with optimization problems where the computation of the gradient of the objective…

In this chapter, we discuss recent advances and new opportunities through methods of machine learning for the field of classical density functional theory, dealing with the equilibrium properties of thermal nano- and micro-particle systems…

We derive a generalized gradient approximation to the exchange energy to be used in density functional theory calculations of two-dimensional systems. This class of approximations has a long and successful history, but it has not yet been…

The main obstacle for practical quantum technology is the noise, which can induce the decoherence and destroy the potential quantum advantages. The fluctuation of a field, which induces the dephasing of the system, is one of the most common…

The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular,…