Symmetry classification of uniform states in spin-2 Bose-Einstein condensates and neutron $^3P_2$ superfluids

TL;DR

This paper establishes a connection between the energy functionals of spin-2 Bose-Einstein condensates and neutron superfluids, classifies their uniform states based on symmetry, and uses geometric invariant theory for analysis.

Contribution

It introduces a unified framework linking Bose-Einstein condensates and neutron superfluids, providing a comprehensive symmetry classification of their uniform states.

Findings

Unified description of spin-2 BECs and neutron superfluids

Complete classification of uniform states by symmetry

Application of geometric invariant theory to quantum fluids

Abstract

We clarify a relation between the Gross-Pitaevskii energy functional for spin-2 spinor Bose-Einstein condensates and the Ginzburg-Landau theory for neutron $^3P_2$ superfluidis (spin-triplet $P$-wave pairing with total angular momentum two). We then classify all uniform states with nontrivial unbroken symmetries, with the help of geometric invariant theory.