Related papers: Quantum Algebraic Symmetries in Nuclei and Molecul…
There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite irreducible…
We discuss various algebraic quantum structures associated to monotone Lagrangian submanifolds and we present a number of applications, computations and examples.
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…
The single-particle spectrum of deformed shell-model states in nuclei, is shown to exhibit a supersymmetric pattern. The latter involves deformed pseudospin doublets and intruder levels. The underlying supersymmetry is associated with the…
We give a modern geometric viewpoint on anomalies in quantum field theory and illustrate it in a 1-dimensional theory: supersymmetric quantum mechanics. This is background for the resolution of worldsheet anomalies in orientifold…
Structure and reaction studies with a method of antisymmetrized molecular dynamics (AMD) were reviewed. Applications of time-independent and time-dependent versions of the AMD were described. In applications of time-independent AMD to…
Nuclear physics, whose underling theory is described by quantum gauge field coupled with matter, is fundamentally important and yet is formidably challenge for simulation with classical computers. Quantum computing provides a perhaps…
A family of geometric models of quantum relativistic rotating oscillator is defined by using a set of one-parameter deformations of the static (3+1) de Sitter or anti-de Sitter metrics. It is shown that all these models lead to the usual…
The strong force that binds atomic nuclei is governed by the rules of Quantum Chromodynamics. Here we consider the suggestion the internal quark structure of a nucleon will adjust self-consistently to the local mean scalar field in a…
In this introductory review, we focus on applications of quantum computation to problems of interest in physics and chemistry. We describe quantum simulation algorithms that have been developed for electronic-structure problems,…
We apply the Anharmonic Oscillator Symmetry Model to the description of vibrational excitations in ${\cal D}_{3h}$ and ${\cal T}_d$ molecules. A systematic procedure can be used to establish the relation between the algebraic and…
A random matrix model to describe the coupling of $m$-fold symmetry is constructed. The particular threefold case is used to analyze data on eigenfrequencies of elastomechanical vibration of an anisotropic quartz block. It is suggested that…
Two planar supersymmetric quantum mechanical systems built around the quantum integrable Kepler/Coulomb and Euler/Coulomb problems are analyzed in depth. The supersymmetric spectra of both systems are unveiled, profiting from symmetry…
Molecular vibrations underpin important phenomena such as spectral properties, energy transfer, and molecular bonding. However, obtaining a detailed understanding of the vibrational structure of even small molecules is computationally…
In this paper, the application of quantum simulations and quantum machine learning to solve low-energy nuclear physics problems is explored. The use of quantum computing to deal with nuclear physics problems is, in general, in its infancy…
We study some basic quantum confinement effects through investigation a deformed harmonic oscillator algebra. We show that spatial confinement effects on a quantum harmonic oscillator can be represented by a deformation function within the…
Background: Symmetries are a powerful way to characterize nuclear wave functions. A true dynamical symmetry, where the Hamiltonian is block-diagonal in subspaces defined by the group, is rare. More likely is a quasidynamical symmetry:…
Quantum geometry, describing the geometric properties of the Bloch wave function in momentum space, has recently been recognized as a fundamental concept in condensed matter physics. The flat-band system offers the paradigmatic platform…
Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation…
Deformation quantization and geometric quantization on K\"ahler manifolds give the mathematical description of the algebra of quantum observables and the Hilbert spaces respectively, where the later forms a representation of quantum…