Related papers: Spectrum Generating Algebra for X$_{3}$ Molecules
Introduction: molecular geometry, the three-dimensional arrangement of atoms within a molecule, is fundamental to understanding chemical reactivity, physical properties, and biological activity. The prevailing models used to describe…
We consider harmonics generation and wave-mixing by two-color multi photon resonant excitation of three-level atoms/molecules in strong laser fields. The coherent part of the spectra corresponding to multicolor harmonics generation is…
The dynamics of non-polar diatomic molecules interacting with a far-detuned narrow-band laser field, that only may drive rotational transitions, is studied. The rotation of the molecule is considered both classically and quantum…
Given a finite, simple, vertex-weighted graph, we construct a graded associative (non-commutative) algebra, whose generators correspond to vertices and whose ideal of relations has generators that are graded commutators corresponding to…
Line-by-line calculations are becoming the standard procedure for carrying spectral simulations. However, it is important to insure the accuracy of such spectral simulations through the choice of adapted models for the simulation of key…
Recent advances in machine learning for molecules exhibit great potential for facilitating drug discovery from in silico predictions. Most models for molecule generation rely on the decomposition of molecules into frequently occurring…
In this paper, a new class of band matrices is considered where the entries of each non-zero band form a sequence with two limit points. The compact perturbation technique is used to study the spectrum over the $\ell_{p}, (1<p<\infty)$…
We study the non-singlet sectors of matrix quantum mechanics (MQM) through an operator algebra which generates the spectrum. The algebra is a nonlinear extension of the W_\infty algebra where the nonlinearity comes from the angular part of…
We develop a framework to describe a wide class of flat-band models, with and without a translational symmetry, by using "molecular orbitals" introduced in the prior work (HATSUGAI Y. and MARUYAMA I., \textit{EPL}, \textbf{95}, (2011)…
The main motivation for this work is the exploration of rotational-vibrational states corresponding to electronic excitations in a pre-Born-Oppenheimer quantum theory of molecules. These states are often embedded in the continuum of the…
Geometric representation-conditioned molecule generation provides an effective paradigm that decouples molecule representation modeling from structure generation. By decoupling molecule generation into two stages-first generating a…
We investigate the properties of the inverse limit of the algebras of local unitary invariant polynomials of quantum systems containing various types of fermionic and/or bosonic particles as the dimensions of the single particle state…
The finite dimensional representations of associative quadratic algebras with three generators are investigated by using a technique based on the deformed parafermionic oscillator algebra. One application on the calculation of the…
The polynomial algebra is a deformed SU(2) algebra. Here, we use polynomial algebra as a method to solve a series of deformed oscillators. Meanwhile, we find a series of physics systems corresponding with polynomial algebra with different…
We construct integrable generalised models in a systematic way exploring different representations of the gl(N) algebra. The models are then interpreted in the context of atomic and molecular physics, most of them related to different types…
A way to construct and classify the three dimensional polynomially deformed algebras is given and the irreducible representations is presented. for the quadratic algebras 4 different algebras are obtained and for cubic algebras 12 different…
A scheme based on a unifying q-deformed algebra and associated with a generalized Lax operator is proposed for generating integrable quantum and statistical models. As important applications we derive known as well as novel quantum models…
Universal algebraic geometry is generalised from solutions of equations in a single algebra to the study of $\varphi$- or $K$-spectra, akin to the prime spectrum of a ring. We explore their basic properties and constructions, give a…
All possible Lie bialgebra structures on the harmonic oscillator algebra are explicitly derived and it is shown that all of them are of the coboundary type. A non-standard quantum oscillator is introduced as a quantization of a triangular…
We present simulations of peak pattern formation in vibrated two-dimensional (2D) granulates and measure the dispersion relation of the pattern for various frequencies, accelerations, cell sizes, and layer heights. We report the first…