Related papers: A step toward density benchmarking -- the energy-r…
Recent advances in modeling density distributions, so-called neural density fields, can accurately describe the density distribution of celestial bodies without, e.g., requiring a shape model - properties of great advantage when designing…
Linear-scaling implementations of density functional theory (DFT) reach their intended efficiency regime only when applied to systems having a physical size larger than the range of their Kohn-Sham density matrix (DM). This causes a problem…
Predictions of observable properties by density-functional theory calculations (DFT) are used increasingly often in experimental condensed-matter physics and materials engineering as data. These predictions are used to analyze recent…
The mean-field approximations of many-boson dynamics are known to be effective in many physical relevant situations. The mathematical justifications of such approximations rely generally on specific considerations which depend too much on…
Many real-world phenomena can be modelled as dynamical processes on networks, a prominent example being the spread of infectious diseases such as COVID-19. Mean-field approximations are a widely used tool to analyse such dynamical processes…
In this work, we aim to solve a practical use-case of unsupervised clustering which has applications in predictive maintenance in the energy operations sector using quantum computers. Using only cloud access to quantum computers, we…
It is well known that mean-field theories fail to reproduce the experimentally known critical exponents. The traditional argument which explain this failure of mean-field theories near a critical point is the Ginsburg criterion in which…
Kernel density estimation is a technique for approximating probability distributions. Here, it is applied to the calculation of mutual information on a metric space. This is motivated by the problem in neuroscience of calculating the mutual…
Density Functional Theory (DFT) is one of the most widely used methods for "ab initio" calculations of the structure of atoms, molecules, crystals, surfaces, and their interactions. Unfortunately, the customary introduction to DFT is often…
Mean-field approaches where a complex fermionic many-body problem is replaced by an ensemble of independent particles in a self-consistent mean-field can describe many static and dynamical aspects. It generally provides a rather good…
The validity of the approximations done in the mean field description of the quasi-elastic excitation of medium-heavy nuclei is discussed. A test of the reliability of the plane wave Born approximation is presented. The uncertainty related…
Nuclear density functional theory (DFT) is the only microscopic, global approach to the structure of atomic nuclei. It is used in numerous applications, from determining the limits of stability to gaining a deep understanding of the…
We investigate an extension of excited state mean-field theory in which the energy expression is augmented with density functional components in an effort to include the effects of weak electron correlations. The approach remains…
Two electrons at the threshold of ionization represent a severe test case for electronic structure theory. A pseudospectral method yields a very accurate density of the two-electron ion with nuclear charge close to the critical value.…
Kernel estimation techniques, such as mean shift, suffer from one major drawback: the kernel bandwidth selection. The bandwidth can be fixed for all the data set or can vary at each points. Automatic bandwidth selection becomes a real…
The main difficulty that arises in the analysis of most machine learning algorithms is to handle, analytically and numerically, a large number of interacting random variables. In this Ph.D manuscript, we revisit an approach based on the…
In this paper, we present an innovative particle system characterized by moderate interactions, designed to accurately approximate kinetic flocking models that incorporate singular interaction forces and local alignment mechanisms. We…
We prove that the electron density function of a real physical system can be uniquely determined by its values on any finite subsystem. This establishes the existence of a rigorous density-functional theory for any open electronic system.…
Photons mediate long-range optomechanical forces between atoms in high finesse resonators, which can induce the formation of ordered spatial patterns. When a transverse laser drives the atoms, the system undergoes a second order phase…
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus…