Related papers: Spectrum Generating Algebra for X$_{3}$ Molecules
We propose a method, based on a Generalized Heisenberg Algebra (GHA), to reproduce the anharmonic spectrum of diatomic molecules. The theoretical spectrum generated by GHA allows us to fit the experimental data and to obtain the…
In this paper, we present the quadratic associative symmetry algebra of the 3D nondegenerate maximally quantum superintegrable system. This is the complete symmetry algebra of the system. It is demonstrated that the symmetry algebra…
High-order harmonic generation is a powerful and sensitive tool for probing atomic and molecular structures, combining in the same measurement an unprecedented attosecond temporal resolution with a high spatial resolution, of the order of…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
A new physical implementation for quantum computation is proposed. The vibrational modes of molecules are used to encode qubit systems. Global quantum logic gates are realized using shaped femtosecond laser pulses which are calculated…
$C_{\lambda}$-extended oscillator algebras, generalizing the Calogero-Vasiliev algebra, where $C_{\lambda}$ is the cyclic group of order $\lambda$, have recently proved very useful in the context of supersymmetric quantum mechanics and some…
We discuss a symmetry-adapted algebraic (or vibron) model for molecular spectroscopy. The model is formulated in terms of tensor operators under the molecular point group. In this way, we have identified interactions that are absent in…
A beam of diatomic molecules scattered off a standing wave laser mode splits according to the rovibrational quantum state of the molecules. Our numerical calculation shows that single state resolution can be achieved by properly tuned,…
The system of two $Q$-deformed oscillators coupled so that the total Hamiltonian has the su$_Q$(2) symmetry is proved to be equivalent, to lowest order approximation, to a system of two identical Morse oscillators coupled by the…
We study how to generate molecule conformations (i.e., 3D structures) from a molecular graph. Traditional methods, such as molecular dynamics, sample conformations via computationally expensive simulations. Recently, machine learning…
We present an algebraic U(7) model for baryons which encompasses both single-particle and collective forms of quark dynamics. The mass operator by construction preserves the permutation symmetry between identical quarks. The underlying…
In this paper we demonstrate how asymmetric molecular rotational spectra may be introduced to students both "pictorially" and with simple formulae. It is shown that the interpretation of such spectra relies heavily upon pattern recognition.…
We present Symphony, an $E(3)$-equivariant autoregressive generative model for 3D molecular geometries that iteratively builds a molecule from molecular fragments. Existing autoregressive models such as G-SchNet and G-SphereNet for…
With the recent advances in machine learning for quantum chemistry, it is now possible to predict the chemical properties of compounds and to generate novel molecules. Existing generative models mostly use a string- or graph-based…
A very efficient large-order perturbation theory is formulated for the nuclear motion of a linear triatomic molecule. To demonstrate the method, all of the experimentally observed rotational energies, with values of $J$ almost up to 100,…
Discovery of atomistic systems with desirable properties is a major challenge in chemistry and material science. Here we introduce a novel, autoregressive, convolutional deep neural network architecture that generates molecular equilibrium…
Algebraic models are proposed for the description of the shell-like quarteting of the nucleons both on the phenomenologic and on the semimicroscopic levels. In the previous one the quartet is considered as a structureless object, while in…
We construct a generalisation of the three-dimensional Poincar\'e algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincar\'e gravity in three space-time dimensions as well as to study…
We propose an accurate and efficient method to compute vibrational spectra of molecules, based on exact diagonalization of an algebraically calculated matrix based on powers of Morse coordinate. The present work focuses on the 1D potential…
A rotor system, having the symmetry afforded by the two-parameter quantum algebra Uqp(u(2)), is investigated in this communication. This system is useful in rotational spectroscopy of molecules and nuclei. In particular, it is shown to lead…