Related papers: Spectrum Generating Algebra for X$_{3}$ Molecules
Developing the analysis of the distribution of the so-called posmom xp to the spherical harmonics that represents some molecular rotational states for such as diatomic molecules and spherical cage molecules, we obtain posmometry (introduced…
Using a quantum mechanical three-step model we present numerical calculations on the high-harmonic generation from four polyatomic molecules. Ethylene (C$_2$H$_4$) serves as an example where orbital symmetry directly affects the harmonic…
The symmetry algebra of the N-dimensional anisotropic quantum harmonic oscillator with rational ratios of frequencies is constructed by a method of general applicability to quantum superintegrable systems. The special case of the 3-dim…
A two-parameter quantum algebra $U_{qp}({\rm u}_2)$ is briefly investigated in this paper. The basic ingredients of a model based on the $U_{qp}({\rm u}_2)$ symmetry, the $qp$-rotator model, are presented in detail. Some general tendencies…
Recent advances in artificial intelligence have propelled the development of innovative computational materials modeling and design techniques. Generative deep learning models have been used for molecular representation, discovery, and…
The least upper bound on degrees of elements of a minimal system of generators of the algebra of invariants of 3x3 matrices is found, and the nilpotency degree of a relatively free finitely generated algebra with the identity x^3=0 is…
In this work we develop a mathematical formalism which allows obtaining oscillation formula for neutrino of any energy. We demonstrate that in the ultra-relativistic limit the results obtained in this new approach agree with the previously…
Benchmarks of molecular machine learning models often treat the molecular representation as a neutral input format, yet the representation defines the syntax of validity, edit operations, and invariances that models implicitly learn. We…
A three step model for high harmonic generation from impurities in solids is developed. The process is found to be similar to high harmonic generation in atomic and molecular gases with the main difference coming from the non-parabolic…
The problem of correlation between quantum states of four-atomic molecules in different geometrical configurations is reviewed in detail. A general, still simple rule is obtained which allows one to correlate states of a linear four-atomic…
A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a…
We present a systematic understanding of the rotational structure of a long-range (vibrationally highly-excited) diatomic molecule. For example, we show that depending on a quantum defect, the least-bound vibrational state of a diatomic…
We obtain results describing the behavior of the action of rotation generators on polynomials over a commutative ring. We also explore harmonic polynomials in a purely algebraic setting.
The algebraic molecular model is used in $^{12}$C to construct densities and transition densities connecting low-lying states of the rotovibrational spectrum, first and foremost those belonging to the rotational bands based on the ground…
The computation of vibrational spectra of diatomic molecules through the exact diagonalization of algebraically determined matrixes based on powers of Morse coordinates is made substantially more efficient by choosing a properly adapted…
Different generators of a deformed oscillator algebra give rise to one-parameter families of $q$-exponential functions and $q$-Hermite polynomials related by generating functions. Connections of the Stieltjes and Hamburger classical moment…
We use the mathematical structure of group algebras and $H^{+}$-algebras for describing certain problems concerning the quantum dynamics of systems of angular momenta, including also the spin systems. The underlying groups are ${\rm SU}(2)$…
The rotation vibration spectra of small molecules can be described mathematically completely. Unfortunately, no vivid interpretation of the observed transitions exists. A qualitative interpretation attempt is undertaken for symmetric top…
A three-parametric $R$-matrix satisfying a graded Yang-Baxter equation is introduced.This $R$-matrix allows us to construct new quantum supergroups which are deformations of the supergroup $GL(1/1)$ and the universal enveloping algebra…
The rational design of molecules with desired properties is a long-standing challenge in chemistry. Generative neural networks have emerged as a powerful approach to sample novel molecules from a learned distribution. Here, we propose a…