Related papers: Natural orbitals for many-body expansion methods
We study the quantum mechanical many-body problem of $N \geq 1$ non-relativistic electrons with spin interacting with their self-generated classical electromagnetic field and $K \geq 0$ static nuclei. We model the dynamics of the electrons…
The reduced basis method is used to construct a "universal" basis of Dirac orbitals that may be applicable throughout the nuclear chart to calibrate covariant energy density functionals. Relative to our earlier work using the…
The Many-Body Expansion (MBE) is a useful tool to simulate condensed phase chemical systems, often avoiding the steep computational cost of usual electronic structure methods. However, it often requires higher than 2-body terms to achieve…
In recent years, stable and unstable manifolds of invariant objects (such as libration points and periodic orbits) have been increasingly recognized as an efficient tool for designing transfer trajectories in space missions. However, most…
A new convenient method to diagonalize the non-relativistic many-body Schroedinger equation with two-body central potentials is derived. It combines kinematic rotations (democracy transformations) and exact calculation of overlap integrals…
The construction of predictive models of atomic nuclei from first principles is a challenging (yet necessary) task towards the systematic generation of theoretical predictions (and associated uncertainties) to support nuclear data…
This study introduces a novel approach for deriving the governing equations of the musculoskeletal system in the human body. The proposed formalism offers a framework to effectively incorporate the kinematic characteristics of biological…
The reach of ab initio many-body theories is rapidly extending over the nuclear chart. However, dealing fully with three-nucleon, possibly four-nucleon, interactions makes the solving of the A-body Schr\"odinger equation particularly…
The relativistic 2-body problem, much like the non-relativistic one, is reduced to describing the motion of an effective particle in an external field. The concept of a relativistic reduced mass and effective particle energy introduced some…
In this paper we present in detail Newton's method and its modification, based on the Continuous analog of Newton's method for computing periodic orbits of the planar three-body problem. The linear system at each step of the method is…
Inspiralling and coalescing binary black holes are promising sources of gravitational radiation. The orbital motion and gravitational-wave emission of such system can be modelled using a variety of approximation schemes and numerical…
Theoretical approaches to nonequilibrium many-body dynamics generally rest upon an adiabatic assumption, whereby the true dynamics is represented as a sequence of equilibrium states. Going beyond this simple approximation is a notoriously…
A numerically implementable Multi-scale Many-Body approach to strongly correlated electron systems is introduced. An extension to quantum cluster methods, it approximates correlations on any given length-scale commensurate with the strength…
Whether for fundamental studies or nuclear data evaluations, first-principle calculations of atomic nuclei constitute the path forward. Today, performing \textit{ab initio} calculations (a) of heavy nuclei, (b) of doubly open-shell nuclei…
A simple yet general method for constructing basis sets for molecular electronic structure calculations is presented. These basis sets consist of atomic natural orbitals from a multi-configurational self-consistent field calculation…
We investigate a singularly perturbed, non-convex variational problem arising in materials science with a combination of geometrical and numerical methods. Our starting point is a work by Stefan M\"uller, where it is proven that the…
We present a numerical framework for modeling extended hyperelastic bodies based on a Lagrangian formulation of general relativistic elasticity theory. We use finite element methods to discretize the body, then use the semi--discrete action…
The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three…
High-precision predictions of nuclear properties are a central objective of ab initio nuclear structure theory. However, state-of-the-art many-body methods rely on truncated model spaces to render the nuclear many-body problem tractable,…
We introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled…