Partial dynamical symmetries in quantum systems

TL;DR

This paper introduces the concept of partial dynamical symmetries in quantum systems, showing how certain Hamiltonians exhibit symmetry in some states but not others, with implications for nuclear spectroscopy and phase transitions.

Contribution

It provides an explicit construction of Hamiltonians with partial dynamical symmetries, including higher-order terms, and explores their significance in nuclear physics.

Findings

Identification of single and multiple PDSs in nuclear models

Implications for spectroscopy and shape-phase transitions

Construction of Hamiltonians with partial symmetries

Abstract

We discuss the the notion of a partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by only a subset of solvable eigenstates, while other eigenstates are strongly mixed. We present an explicit construction of Hamiltonians with this property, including higher-order terms, and portray their significance for spectroscopy and shape-phase transitions in nuclei. The occurrence of both a single PDS, relevant to stable structures, and of several PDSs, relevant to coexistence phenomena, are considered.