Three-fluid hydrodynamics of spin-1 Bose-Einstein condensates

Abstract

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 coupled linear hydrodynamic equations of the three sounds and evaluate them numerically in a self-consistent mean-field approximation valid for dilute gas in the intermediate and critical temperature regions. In this latter region we identify the critical mode.