Related papers: Spectrum Generating Algebra for X$_{3}$ Molecules
We show that for any finitely generated non-amenable group and any $\varepsilon>0$, there exists some finite symmetric generating set with spectral radius less than $\varepsilon$. We give applications to percolation theory and the theory of…
In the first work of this series [physics/0204035] it was shown that the conformational space of a molecule could be described to a fair degree of accuracy by means of a central hyperplane arrangement. The hyperplanes divide the espace into…
We describe an inexpensive instructional experiment that demonstrates the rotational energy levels of diatomic nitrogen, using the emission band spectrum of molecular nitrogen ionized by various processes in a commercial AC capillary…
Semiconductor superlattice multipliers have emerged as a nonlinear medium capable to generate radiation in a wide frequency range. This property facilitates the potential of sources suitable for sensing and spectroscopy applications. In…
In quantum mechanics, associative algebras play an important role in understanding symmetries and operator algebras, providing new algebraic frameworks for describing physical systems. This work classifies associative algebras over a field…
We analytically tackle opto-vibronic interactions in molecular systems driven by either classical or quantum light fields. In particular, we examine a simple model of molecules with two relevant electronic levels, characterized by potential…
We present the graph-based molecule software Molassembler for building organic and inorganic molecules. Molassembler provides algorithms for the construction of molecules built from any set of elements from the periodic table. In…
Molecules are frequently represented as graphs, but the underlying 3D molecular geometry (the locations of the atoms) ultimately determines most molecular properties. However, most molecules are not static and at room temperature adopt a…
Using vertex algebra techniques, we determine a set of generators for the cohomology ring of the Hilbert schemes of points on an arbitrary smooth projective surface over the field of complex numbers.
A general framework for the kinetic modelling of non-relativistic polyatomic gases is proposed,where each particle is characterized both by its velocity and by its internal state, and the Boltzmann collisionoperator involves suitably…
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
Graded skew-commutative rings occur often in practice. Here are two examples: 1) The cohomology ring of a compact three-dimensional manifold. 2) The cohomology ring of the complement of a hyperplane arrangement (the Orlik-Solomon algebra).…
An algebraic model taking into account the influence of the molecular rotation on the wave functions of vibrational-rotational states of the diatomic molecule using the formalism of the ladder operators and an expansion in a small parameter…
We present a generator of virtual molecules that selects valid chemistry on the basis of the octet rule. Also, we introduce a mesomer group key that allows a fast detection of duplicates in the generated structures. Compared to existing…
This paper illustrates the application of group theory to a quantum-mechanical three-dimensional quartic anharmonic oscillator with $O_{h}$ symmetry. It is shown that group theory predicts the degeneracy of the energy levels and facilitates…
Quantum beats in nonlinear spectroscopy of molecular aggregates are often attributed to electronic phenomena of excitonic systems, while nuclear degrees of freedom are commonly included into models as overdamped oscillations of bath…
We propose a new model for the description of complex granular particles and their interaction in molecular dynamics simulations of granular material in two dimensions. The grains are composed of triangles which are connected by deformable…
A rotational model is developed from a new version of the two-parameter quantum algebra $U_{qp}({\rm u}_2)$. This model is applied to the description of some recent experimental data for the rotating superdeformed nuclei…
We introduce a $Z_3$-graded version of exterior (Grassmann) algebra with two generators and using this object we obtain a new $Z_3$-graded quantum group denoted by $O(\widetilde{GL}_q(2))$. We also discuss some properties of ${…
Molecular representation learning has attracted much attention recently. A molecule can be viewed as a 2D graph with nodes/atoms connected by edges/bonds, and can also be represented by a 3D conformation with 3-dimensional coordinates of…