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

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 3 P2 superfluidis (spin-triplet P -wave paring with total angular momentum two). We then classify all uniform states with nontrivial unbroken symmetries, with a help of the geometric invariant theory.