Exact Dynamical and Partial Symmetries

TL;DR

This paper explores a hierarchy of broken symmetries, focusing on partial dynamical symmetries (PDS), and presents an algorithm for constructing Hamiltonians with these properties, relevant to nuclear physics and quantum systems.

Contribution

It introduces a novel algorithm for creating Hamiltonians exhibiting partial dynamical symmetries, linking symmetry concepts to physical phenomena.

Findings

PDS allows some eigenstates to retain symmetry while others are mixed.

The algorithm effectively constructs Hamiltonians with desired symmetry properties.

PDS applications include nuclear spectroscopy and quantum phase transitions.

Abstract

We discuss a hierarchy of broken symmetries with special emphasis on partial dynamical symmetries (PDS). The latter correspond to a situation in which a non-invariant Hamiltonian accommodates a subset of solvable eigenstates with good symmetry, while other eigenstates are mixed. We present an algorithm for constructing Hamiltonians with this property and demonstrate the relevance of the PDS notion to nuclear spectroscopy, to quantum phase transitions and to mixed systems with coexisting regularity and chaos.