Dynamical Symmetries and Beyond: Lessons and Advances

Abstract

A central theme in Iachello's quest for understanding simple ordered patterns in complex quantum systems, is the concept of dynamical symmetry. Relying on his seminal contributions, we present further generalization of this notion to that of partial dynamical symmetry (PDS), for which solvability and good quantum numbers are maintained by only a subset of states. Hamiltonians with a single PDS and multiple PDSs are constructed explicitly and their relevance to nuclear structure is discussed.

10 pages, 9 figures, Proc. Int. Symposium on "Symmetries and Order: Algebraic Methods in Many Body Systems", in honor of Professor Francesco Iachello, October 5-6, 2018 at Yale University

References in corpus (7)

• Partial Dynamical Symmetry at Critical-Points of Quantum Phase Transitions
• Partial dynamical symmetry in quantum Hamiltonians with higher-order terms
• First-order quantum phase transitions: test ground for emergent chaoticity, regularity and persisting symmetries
• Partial dynamical symmetry as a selection criterion for many-body interactions
• Algebraic benchmark for prolate-oblate coexistence in nuclei
• Partial dynamical symmetries and shape coexistence in nuclei
• Partial dynamical symmetry in Bose-Fermi systems