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The nuclear many-body problem for medium-mass systems is commonly addressed using wave-function expansion methods that build upon a second-quantized representation of many-body operators with respect to a chosen computational basis. While…
Natural orbitals, defined in electronic structure and quantum chemistry as the (molecular) orbitals diagonalizing the one-particle reduced density matrix of the ground state, have been conjectured for decades to be the perfect reference…
Ordinal embedding aims at finding a low dimensional representation of objects from a set of constraints of the form "item $j$ is closer to item $i$ than item $k$". Typically, each object is mapped onto a point vector in a low dimensional…
A simple procedure is developed to determine orbital elements of an object orbiting in a central force field which contribute more than three independent celestial positions. By manipulation of formal three point Gauss method of orbit…
The magnetic response of strongly localized electrons to a time-dependent vector potential is considered. The orbital magnetic moment of the system, away from steady-state conditions, is obtained. The expression involves the tunneling and…
A flexible wave localization is investigated using a spatial-temporal modulation of point defects along the periodic array of electromechanical local resonators of a piezoelectric bimorph beam. By changing the electrical resonance of…
We investigate the suitability of natural orbitals as a basis for describing many-body excitations. We analyze to which extend the natural orbitals describe both bound as well as ionized excited states and show that depending on the…
Anderson localization of classical waves in disordered media is a fundamental physical phenomenon that has attracted attention in the past three decades. More recently, localization of polar excitations in nanostructured metal-dielectric…
The implementation of the orbital minimization method (OMM) for solving the self-consistent Kohn-Sham (KS) problem for electronic structure calculations in a basis of non-orthogonal numerical atomic orbitals of finite-range is reported. We…
In this contribution we present a survey of concepts in localized model order reduction methods for parameterized partial differential equations. The key concept of localized model order reduction is to construct local reduced spaces that…
A new material characterization technique is emerging for the transmission electron microscope (TEM). Using electron energy-loss spectroscopy, real space mappings of the underlying electronic transitions in the sample, so called orbital…
In electronic structure theory, variational methods offer a valuable paradigm for approximating electronic ground states. However, for historical reasons, this principle is mostly restricted to model chemistries in pre-defined fixed basis…
The location of electrons governs phenomena ranging from chemical bonding and electric polarization to the topological classification of band insulators and the emergence of correlated states in quantum matter. While a prescription exists…
The Wigner localization is an electron phase at low densities when the electrons are sharply localized around equilibrium positions. The simulation of the Wigner localization phenomenon requires careful treatment of the many-body…
Machine learning has become a promising approach for molecular modeling. Positional quantities, such as interatomic distances and bond angles, play a crucial role in molecule physics. The existing works rely on careful manual design of…
We improved a previously proposed method of using closed-orbit modulation for linear optics correction. Instead of fitting individual closed orbits, the improved method decomposes the orbit oscillation data into two orthogonal modes and…
Scientists use imaging to identify objects of interest and infer properties of these objects. The locations of these objects are often measured with error, which when ignored leads to biased parameter estimates and inflated variance.…
Construction of hybrid atomic orbitals is proposed as the approximate common eigen states of finite first moment matrices. Their hybridization and orientation can be a-priori tunned as per their anticipated neighbourhood. Their Wannier…
Orthogonality constraints naturally appear in many machine learning problems, from principal component analysis to robust neural network training. They are usually solved using Riemannian optimization algorithms, which minimize the…
We consider diatomic systems in which the kinetic energy of the electrons is treated in a simple relativistic model. The Born-Oppenheimer approximation is assumed. We investigate questions of stability, deducing bounds on the number $N$ of…