Quantum catastrophes from an algebraic perspective

Abstract

We study the properties of quantum cusp and butterfly catastrophes from an algebraic viewpoint. The analysis employs an interacting boson model Hamiltonian describing quantum phase transitions between specific quadrupole shapes by interpolating between two incompatible dynamical symmetry limits. The classical properties are determined by using coherent states to construct the complete phase diagrams associated with Landau potentials exhibiting such catastrophes.The quantum properties are determined by analyzing the spectra, transition rates and symmetry character of the eigenstates of critical Hamiltonians.

arXiv comment14 pages, 11 figures, talk at Symposium "Symmetries in Science XVIII", August 4-9, 2019, Bregenz, Austria

References in corpus (26)

• Quantum phase transitions in the interacting boson model
• Partial Dynamical Symmetry in Deformed Nuclei
• Impact of Quantum Phase Transitions on Excited Level Dynamics
• The U(5)-O(6) transition in the Interacting Boson Model and the E(5) critical point symmetry
• Partial Dynamical Symmetries
• Partial Dynamical Symmetry at Critical-Points of Quantum Phase Transitions
• Phase transitions and critical points in the rare-earth region
• Evolution of spectral properties along the O(6)-U(5) transition in the interacting boson model. I. Level dynamics
• Critical-Point Symmetry in a Finite System
• Quadrupole Phonons in the Cadmium Isotopes
• Partial dynamical symmetry in quantum Hamiltonians with higher-order terms
• Finite-size scaling exponents in the interacting boson model
• Evolution of spectral properties along the O(6)-U(5) transition in the interacting boson model. II. Classical trajectories
• Partial Dynamical SU(3) Symmetry and the Nature of the Lowest K=0 Collective Excitation in Deformed Nuclei
• The ${\beta }^4$ potential at the U(5)-O(6) critical point of the Interacting Boson Model
• Partial Dynamical Symmetry and Mixed Dynamics
• 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
• Entanglement in quantum catastrophes
• Criticality in the configuration-mixed interacting boson model : (1) $U(5)-\hat{Q}(\chi )\cdot \hat{Q}(\chi )$ mixing
• Partial dynamical symmetries and shape coexistence in nuclei
• Phase diagram of the two-fluid Lipkin model: a butterfly catastrophe
• Disentangling phase transitions and critical points in the proton-neutron interacting boson model by catastrophe theory
• Coexisting partial dynamical symmetries and multiple shapes
• Partial dynamical symmetries in quantum systems

Cited by in corpus (2)

• Application of the cranking method to the semimicroscopic algebraic cluster model and nuclear molecules
• Quantum Phase Transitions within a nuclear cluster model and an effective model of QCD