Three fluid hydrodynamics of spin-1 Bose-Einstein condensates
  We study excitations of the spin-1 Bose gas at finite temperatures and in the presence of a not so strong magnetic field, or equivalently, when the gas sample is partially polarized. Motivated by the success of two-fluid hydrodynamics of scalar superfluids we develop a three-fluid hydrodynamic description to treat the low frequency and long wavelength excitations of the spin-1 Bose gas. We derive the coupled linear hydrodynamic equations of the three sounds and evaluate them numerically in a self-consistent mean field approximation valid for the dilute gas at the intermediate and critical temperature regions. In this latter region we identify the critical mode. 
Gergely Szirmai and Peter Szepfalusy
cond-mat.quant-gas quant-ph