Partial Dynamical Symmetries

Abstract

This overview focuses on the notion of partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by a subset of solvable eigenstates, but is not shared by the Hamiltonian. General algorithms are presented to identify interactions, of a given order, with such intermediate-symmetry structure. Explicit bosonic and fermionic Hamiltonians with PDS are constructed in the framework of models based on spectrum generating algebras. PDSs of various types are shown to be relevant to nuclear spectroscopy, quantum phase transitions and systems with mixed chaotic and regular dynamics.

74 pages, 22 figures, published version, Progress in Particle and Nuclear Physics

References in corpus (8)

• Quantum phase transitions in the interacting boson model
• Partial conservation of seniority and nuclear isomerism
• Partial Dynamical Symmetry at Critical-Points of Quantum Phase Transitions
• Partial dynamical symmetry in quantum Hamiltonians with higher-order terms
• Construction of SO(5)>SO(3) spherical harmonics and Clebsch-Gordan coefficients
• Partial Dynamical Symmetries in the g9/2 Shell-Progress and Puzzles
• Relations Between Coefficients of Fractional Parentage
• Solvability of eigenvalues in jn configurations

Cited by in corpus (43)

• Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars
• Dual pairing of symmetry groups and dynamical groups in physics
• Isospin mixing and the continuum coupling in weakly bound nuclei
• Shape coexistence in even-even nuclei: A theoretical overview
• Partial conservation of seniority in $j=9/2$ shell: Analytic and numerical studies
• Quadrupole Phonons in the Cadmium Isotopes
• Ermakov-Lewis symmetry in photonic lattices
• First-order quantum phase transitions: test ground for emergent chaoticity, regularity and persisting symmetries
• Proton decays in ${}^{16}$Ne and ${}^{18}$Mg and isospin-symmetry breaking in carbon isotopes and isotones
• Partial dynamical symmetry as a selection criterion for many-body interactions
• Symmetries and deformations in the spherical shell model
• Algebraic benchmark for prolate-oblate coexistence in nuclei
• Partial conservation of seniority and its unexpected influence on E2 transitions in $g_{9/2}$ nuclei
• Linking partial and quasi dynamical symmetries in rotational nuclei
• Analytic proof of partial conservation of seniority in $j=9/2$ shells
• Calculation of the Thomas-Ehrman shift in ${}^{16}$F and ${}^{15}$O(p,p) cross section with the Gamow shell model
• Manifestation of the Berry phase in the atomic nucleus ${}^{213}$Pb
• Regularity and chaos in 0+ states of the interacting boson model using quantum measures
• Prolate-oblate asymmetric shape phase transition in the interacting boson model with SU (3) higher-order interactions
• Searching for structure beyond parity in the two-qubit Dicke model
• Partial dynamical symmetries and shape coexistence in nuclei
• Mechanism of dynamical phase transitions: The complex-time survival amplitude
• Investigation of low-lying energy spectra for deformed prolate nuclei via partial dynamical SU(3) symmetry
• Low-lying states in even Gd isotopes studied with five-dimensional collective Hamiltonian based on covariant density functional theory
• Persistent vibrational structure in ${}^{110-116}$Cd
• Partial dynamical symmetry in Bose-Fermi systems
• Analytic derivation of an approximate SU(3) symmetry inside the symmetry triangle of the Interacting Boson Approximation model
• Partial dynamical symmetry and the vibrational structure of Cd isotopes
• Understanding Xe isotopes near $A=130$ through the prolate-oblate shape phase transition
• Quantum catastrophes from an algebraic perspective
• Partial dynamical symmetry from energy density functionals
• Boundary dissipative spin chains with partial solvability inherited from system Hamiltonians
• Coexisting partial dynamical symmetries and multiple shapes
• SU(3) partial dynamical symmetry and nuclear shapes
• Partial and quasi dynamical symmetries in quantum many-body systems
• Particle-hole symmetry parameters for nuclei
• Partial dynamical symmetries in quantum systems
• Partial dynamical symmetry and odd-even staggering in deformed nuclei
• Dynamical Symmetries and Beyond: Lessons and Advances
• Order, Chaos and Quasi Symmetries in a First-Order Quantum Phase Transition
• Order, Chaos and (Quasi-) Dynamical Symmetries across 1st-order Quantum Phase Transitions in Nuclei
• Simultaneous occurrence of distinct symmetries in nuclei
• Symmetry Remnants in the Face of Competing Interactions in Nuclei