Related papers: Understanding Radicals via Orbital Parities
The use of Slater-type spinor orbitals in algebraic solution of the Dirac equation is investigated. The one- and two-center integrals constitute the matrix elements arising in generalized eigenvalue equation for one-electron atoms and…
We propose a new approach to the combinatorial interpretations of linearization coefficient problem of orthogonal polynomials. We first establish a difference system and then solve it combinatorially and analytically using the method of…
By decomposing the regular representation of a particular (Heisenberg-like) Lie supergroup into irreducible subspaces, we show that not all of them can be obtained by applying geometric quantization to coadjoint orbits with an even…
We report on a possibility of measuring parity violating effects in radiative neutrino pair emission from metastable atoms; asymmetric angular distribution of emitted photons from oriented atoms and emergent circular polarization. Their…
One of the main open problems in the qualitative theory of real planar differential systems is the study of limit cycles. In this article, we present an algorithmic approach for detecting how many limit cycles can bifurcate from the…
A procedure for the construction and the classification of multilattices in arbitrary dimension is proposed. The algorithm allows to determine explicitly the location of the points of a multilattice given its space group, and to determine…
We introduce orbital graphs and discuss some of their basic properties. Then we focus on their usefulness for search algorithms for permutation groups, including finding the intersection of groups and the stabilizer of sets in a group.
A one-dimensional model of coupled spin-1/2 spins and pseudospin-1/2 orbitals with nearest-neighbor interaction is rigorously shown to exhibit spin-orbital separation by means of a non-local unitary transformation. On an open chain, this…
The well-known spatial integration schemes in molecular electronic structure theory, immune to cusps and point singularities of some kind at atomic positions, use a set of weighting functions to split the integrand into a sum of…
We study the real algebraic variety of real symmetric matrices with eigenvalue multiplicities determined by a partition. We present formulas for the dimension and Euclidean distance degree. We give a parametrization by rational functions.…
Altermagnetism has so far mainly been understood in its even- and odd-parity forms. We show that collinear antiferromagnets with zero net magnetization can also host mixed-parity spin splitting, namely neither purely even nor purely odd in…
Lie symmetries of the Schroedinger-Pauli equations for charged particles and quasirelativistic Schroedinger equations are classified. In particular a new superintegrable system with spin-orbit coupling is discovered.
We investigate using optically trapped linear polyatomic molecules as probes of nuclear spin-dependent parity violation. The presence of closely spaced, opposite-parity $\ell$-doublets is a general feature of such molecules, allowing…
This paper presents a novel formulation and solution of orbit determination over finite time horizons as a learning problem. We present an approach to orbit determination under very broad conditions that are satisfied for n-body problems.…
We determine sets of elements which, under certain conditions, generate an intersection of ideals up to radical.
Ultrarelativistic collisions of black holes are ideal gedanken experiments to study the nonlinearities of general relativity. In this paper we use semianalytical tools to better understand the nature of these collisions and the emitted…
Orbital solutions for binary or multiple stellar systems that combine astrometry (e.g., position angles and angular separations) with spectroscopy (radial velocities) have important advantages over astrometric-only or spectroscopic-only…
We compute the leading order contribution to radiative losses in the case of spinning binaries with aligned spins due to their spin-orbit interaction. The orbital average along hyperboliclike orbits is taken through an appropriate…
The radial distribution function is a characteristic geometric quantity of a point set in Euclidean space that reflects itself in the corresponding diffraction spectrum and related objects of physical interest. The underlying combinatorial…
The purpose of this article is to study the relationship between numerical invariants of certain subspace arrangements coming from reflection groups and numerical invariants arising in the representation theory of Cherednik algebras. For…