Gross-Pitaevskii description of superfluid dynamics at finite temperature: A short review of recent results

The Gross-Pitaevskii equation (GPE) describes the dynamics of superflows and Bose-Einstein Condensates (BEC) at very low temperature. When a truncation of Fourier modes is performed, the resulting truncated GPE (TGPE) can also describe the correct thermal behavior of a Bose gas, as long as all relevant modes are highly occupied [M.J. Davis, S.A. Morgan, K. Burnett, Simulations of Bose fields at finite temperature, Phys. Rev. Lett. 87 (16) (2001) 160402]. We review some of our group's recent GPE- and TGPE-based numerical studies of superfluid dynamics and BEC stability. The relations with experiments are discussed. (C) 2012 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.