Related papers: Spherical-harmonic-analysis-based optimization of …
Kernel approximation with exponentials is useful in many problems with convolution quadrature and particle interactions such as integral-differential equations, molecular dynamics and machine learning. This paper proposes a weighted…
We show that both confined atoms and electron-atom scattering can be described by a unified basis set method. The central idea behind this method is to place the atom inside a hard potential sphere, enforced by a standard Slater type basis…
Squeezing of collective atomic spins has been shown to improve the sensitivity of atomic clocks and magnetometers to levels significantly below the standard quantum limit. In most cases the requisite atom-atom entanglement has been…
We present a machine learning algorithm for the prediction of molecule properties inspired by ideas from density functional theory. Using Gaussian-type orbital functions, we create surrogate electronic densities of the molecule from which…
We present the 2-point function from Fast and Accurate Spherical Bessel Transformation (2-FAST) algorithm for a fast and accurate computation of integrals involving one or two spherical Bessel functions. These types of integrals occur when…
We present a spectral scheme for atomic structure calculations in pseudopotential Kohn-Sham density functional theory. In particular, after applying an exponential transformation of the radial coordinates, we employ global polynomial…
We develop an efficient algorithm for a spatially inhomogeneous matrix-valued quantum Boltzmann equation derived from the Hubbard model. The distribution functions are $2 \times 2$ matrix-valued to accommodate the spin degree of freedom,…
A computation scheme for solving elliptic boundary value problems with axially symmetric confining potentials using different sets of one-parameter basis functions is presented. The efficiency of the proposed symbolic-numerical algorithms…
Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…
A fully analytical approximation for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis…
The ability to directly follow and time resolve the rearrangement of the nuclei within molecules is a frontier of science that requires atomic spatial and few-femtosecond temporal resolutions. While laser induced electron diffraction can…
We present an accurate spectral integral method (SIM) for the analyses of scattering from multiple circular perfect electric conductor (PEC) cylinders. It solves the coupled surface integral equations by using the Fourier series and…
Electronic structure methods for accurate calculation of molecular properties have a high cost that grows steeply with the problem size, therefore, it is helpful to have the underlying atomic basis functions that are less in number but of…
We consider the interaction of electromagnetic radiation of arbitrary polarization with multi-level atoms in a self-consistent manner, taking into account both spatial and temporal dependencies of local fields. This is done by numerically…
Semi-analytic expressions for the electron cyclotron emission (ECE) shape function are developed for arbitrary high harmonics. The integrand of the ${m}^{\mathrm{th}}$ harmonic ECE shape function is fitted with the readily-integrable test…
We demonstrate a fast spin-s spherical harmonic transform algorithm, which is flexible and exact for band-limited functions. In contrast to previous work, where spin transforms are computed independently, our algorithm permits the…
We propose an algorithm for robust recovery of the spherical harmonic expansion of functions defined on the d-dimensional unit sphere $\mathbb{S}^{d-1}$ using a near-optimal number of function evaluations. We show that for any $f \in…
A simple method is outlined for analytic evaluation of the basic 2-electron atomic integral with integrand containing products of atomic s-type Slater orbitals and exponentially correlated function of the form $r_{ij}…
Background: Precise measurements of atomic transitions affected by electron-nucleus hyperfine interactions offer sensitivity to explore basic properties of the atomic nucleus and study fundamental symmetries, including the search for new…
This work proposes four novel hybrid quadrature schemes for the efficient and accurate evaluation of weakly singular boundary integrals (1/r kernel) on arbitrary smooth surfaces. Such integrals appear in boundary element analysis for…