Related papers: Quantum Algebraic Symmetries in Nuclei and Molecul…
A deformation of the harmonic oscillator algebra associated with the Morse potential and the SU(2) algebra is derived using the quantum analogue of the anharmonic oscillator. We use the quantum oscillator algebra or $q$-boson algebra which…
A great deal of research work has been undertaken in the alpha-clustering study since the pioneering discovery, half a century ago, of 12C+12C molecular resonances. Our knowledge of the field of the physics of nuclear molecules has…
Correspondence between classical periodic orbits and quantum shell structure is investigated for a reflection-asymmetric deformed oscillator model as a function of quadrupole and octupole deformation parameters. Periodic orbit theory…
The one-dimensional harmonic oscillator in a box problem is used to introduce the concept of an oblique-basis shell-model theory. The method is applied to nuclei by combining traditional spherical shell-model states with SU(3) collective…
Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of…
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…
The nuclear shell model is one of the prime many-body methods to study the structure of atomic nuclei, but it is hampered by an exponential scaling on the basis size as the number of particles increases. We present a shell-model quantum…
The simulation of chemistry is among the most promising applications of quantum computing. However, most prior work exploring algorithms for block-encoding, time-evolving, and sampling in the eigenbasis of electronic structure Hamiltonians…
The concept of a quantum algebra is made easy through the investigation of the prototype algebras $u_{qp}(2)$, $su_q(2)$ and $u_{qp}(1,1)$. The latter quantum algebras are introduced as deformations of the corresponding Lie algebras~; this…
Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schroedinger type. In contrast to the standard harmonic oscillators such systems exhibit a continuous…
A novel algebraic topology approach to supersymmetry (SUSY) and symmetry breaking in quantum field and quantum gravity theories is presented with a view to developing a wide range of physical applications. These include: controlled nuclear…
Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but…
We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…
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…
The presence of chaos and quantum chaos is shown in two different nuclear systems. We analyze the chaotic behaviour of the classical SU(2) Yang--Mills--Higgs system, and then we study quantum chaos in the nuclear shell model calculating the…
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…
We examine several types of symmetries which are relevant to quantum phase transitions in nuclei. These include: critical-point, quasidynamical, and partial dynamical symmetries.
We discuss here some aspects related to the symmetries of a quantum many-body problem when trying to treat it on a quantum computer. Several features related to symmetry conservation, symmetry breaking, and possible symmetry restoration are…
Let $A$ be the path algebra of a finite acyclic quiver $Q$ over a finite field. We realize the quantum cluster algebra with principal coefficients associated to $Q$ as a sub-quotient of a certain Hall algebra involving the category of…
We present a systematic investigation of antilinear superoperators and their applications in studying open quantum systems, particularly focusing on quantum geometric invariance, entanglement distribution, and symmetry. We study several…