P. S. Turner | Searcharxiv

arXiv2008

Detecting Hidden Differences via Permutation Symmetries

We present a method for describing and characterizing the state of N particles that may be distinguishable in principle but not in practice due to experimental limitations. The technique relies upon a careful treatment of the exchange symmetry of the state among experimentally accessible and experimentally inaccessible degrees of freedom. The approach we present allows a new formalisation of the notion of indistinguishability and can be implemented easily using currently available experimental techniques. Our work is of direct relevance to current experiments in quantum optics, for which we provide a specific implementation.

quant-ph↗

arXiv2005

Vector coherent state theory of the generic representations of so(5) in an so(3) basis

For applications of group theory in quantum mechanics, one generally needs explicit matrix representations of the spectrum generating algebras that arise in bases that reduce the symmetry group of some Hamiltonian of interest. Here we use vector coherent state techniques to develop an algorithm for constructing the matrices for arbitrary finite-dimensional irreps of the SO(5) Lie algebra in an SO(3) basis. The SO(3) subgroup of SO(5) is defined by regarding SO(5) as linear transformations of the five-dimensional space of an SO(3) irrep of angular momentum two. A need for such irreps arises in the nuclear collective model of quadrupole vibrations and rotations. The algorithm has been implemented in MAPLE, and some tables of results are presented.

math-ph↗