Related papers: Quantum Algebraic Symmetries in Nuclei and Molecul…
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…
This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum…
Symmetry is fundamental in the description and simulation of quantum systems. Leveraging symmetries in classical simulations of many-body quantum systems can results in significant overhead due to the exponentially growing size of some…
We prove a general theorem for constructing integral quantum cluster algebras over ${\mathbb{Z}}[q^{\pm 1/2}]$, namely that under mild conditions the integral forms of quantum nilpotent algebras always possess integral quantum cluster…
The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this…
The relationship between the deformed harmonic oscillator and the formation of molecular cluster structures, whereby valence neutrons are exchanged between cluster cores, is examined. It is found that there is a strong connection between…
The symmetries play important roles in physical systems. We study the symmetries of a Hamiltonian system by investigating the asymmetry of the Hamiltonian with respect to certain algebras. We define the asymmetry of an operator with respect…
We introduce supersymmetric extensions of the Hom-Lie deformation of the Virasoro algebra, as realized in the GL(1,1) quantum superspace, for Bloch electron systems under Zeeman effects. The construction is achieved by defining generators…
Advanced atomic magnetometers have made it possible to acquire nuclear magnetic resonance spectra in zero to ultralow magnetic fields. This regime carries the benefit of compact, low-cost instrumentation with reduced spin relaxation effects…
This paper concerns the notion of a symmetric algebra and its generalization to a quasi-symmetric algebra. We study the structure of these algebras in respect to their hull-kernel regularity and existence of some ideals, especially the…
Geometric analogs of Bloch oscillations studied so far have relied on Berry curvature. We show that a weakly inhomogeneous electric field adds a distinct quantum-metric term to semiclassical wavepacket dynamics, generating an oscillatory…
The mathematical apparatus of quantum--mechanical angular momentum (re)coupling, developed originally to describe spectroscopic phenomena in atomic, molecular, optical and nuclear physics, is embedded in modern algebraic settings which…
A particular quantum phase transition (QPT) is studied at excited energies of light nuclei within the Semimicroscopic Algebraic Cluster Model (SACM), using a combination of catastrophe theory and a direct minimization of the potential. A…
Since the pioneering discovery of molecular resonances in the 12C+12C reaction more than half a century ago a great deal of research work has been undertaken in alpha clustering. Our knowledge on physics of nuclear molecules has increased…
Quantum entanglement offers a unique perspective into the underlying structure of strongly-correlated systems such as atomic nuclei. In this paper, we use quantum information tools to analyze the structure of light and medium-mass…
We address quantum systems isospectral to the harmonic oscillator, as those found within the framework of supersymmetric quantum mechanics, as potential resources for continuous variable quantum information. These deformed oscillator…
The simulation of the spectra measured in nuclear magnetic resonance (NMR) spectroscopy experiments is a computationally non-trivial problem which, due to its natural interpretation as a quantum spin problem, maps in a straightforward way…
Quantum computing is emerging as a promising tool in nuclear physics. However, the cost of encoding fermionic operators hampers the application of algorithms in current noisy quantum devices. In this work, we analyze an encoding scheme…
We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the…
It is an interesting and open problem to trace the origin of the pseudospin symmetry in nuclear single-particle spectra and its symmetry breaking mechanism in actual nuclei. In this report, we mainly focus on our recent progress on this…