Related papers: Huygens-Fresnel principle for molecular continuum …
The goal of this effort is to establish the conditions and limits under which the Huygens-Fresnel principle accurately describes diffraction in the Monte Carlo ray-trace environment. This goal is achieved by systematic intercomparison of…
In this paper we analyze a recently proposed approach for the construction of antisymmetric functions for atomic and molecular systems. It is based on the assumption that the main problems with Hartree-Fock wavefunctions stem from their…
An exactly-solvable model of the non-relativistic harmonic oscillator with a position-dependent effective mass is constructed. The model behaves itself as a semi-infinite quantum well of the non-rectangular profile. Such a form of the…
Many signal processing and machine learning applications are built from evaluating a kernel on pairs of signals, e.g. to assess the similarity of an incoming query to a database of known signals. This nonlinear evaluation can be simplified…
Asymptotic expressions for the radial and full wave functions of a three{body bound halo nuclear system with two charged particles in relative coordinates are obtained in explicit form, when the relative distance between two particles tends…
The superposition principle is fundamental to linear wave systems, ensuring that their physical behaviour is independent of the chosen basis representation. While this principle underpins many analytical techniques, including modal…
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 derived here in a systematic way, and for a large class of scaling regimes, asymptotic models for the propagation of internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid…
The ability to perfectly guide surface electromagnetic waves around ultra-sharp corners without back-scattering and radiation is in great demand for various photonic and plasmonic applications. This is fundamentally difficult to realize…
The fusion of $\alpha$ and $^8$Be to produce a $^{12}$C nucleus is a crucial process in nucleosynthesis. In the laboratory, this process can only be studied theoretically as a $^8$Be target or projectile cannot be prepared experimentally.…
The new representation of the Coulomb three-body wave function via the well-known solutions of the separable Coulomb two-centre problem $\phi_j(\xi,\eta)=X_j(\xi)Y_j(\eta)$ is obtained, where $X_j(\xi)$ and $Y_j(\eta)$ are the Coulomb…
The basic ideas of a homotopy-based multiple-variable method is proposed and applied to investigate the nonlinear interactions of periodic traveling waves. Mathematically, this method does not depend upon any small physical parameters at…
Asymptotic solution to many-body wave scattering problem is given in the case of many small scatterers. The small scatterers can be particles whose physical properties are described by the boundary impedances, or they can be small…
The behavior of monochromatic electromagnetic waves in stationary media is shown to be ruled by a frequency dependent function, which we call Wave Potential, encoded in the structure of the Helmholtz equation. Contrary to the common belief…
Huygens' metasurfaces have demonstrated the ability to tailor electromagnetic wavefronts with passive low-profile structures. The fundamental constraint enabling passive and ideally lossless solutions is the conservation of the normal real…
We present a new approach to real-space multiple-scattering theory for molecules and clusters, based on the two-potential (distorted-wave) Lippmann-Schwinger equation formalism. Our approach uses a recently developed form [D. L. Foulis,…
As 2D materials with subwavelength structures, elastic metasurfaces show remarkable abilities to manipulate elastic waves at will through artificial boundary conditions. However, the application prospects of current metasurfaces may be…
We review the diffraction theory for plane waves and establish its connection to the diffraction of Besicovitch almost periodic functions, extending the theory to an unbounded setting and providing explicit formulas. Then, we give an…
A complete discrete set of spherical single-particle wave functions for studies of weakly-bound many-body systems is proposed. The new basis is obtained by means of a local-scale point transformation of the spherical harmonic oscillator…
We present here a new approach to determine an accurate variational wavefunction for general quantum antiferromagnets, completely defined by the requirement to reproduce the simple and well known spin-wave expansion. By this wavefunction,…