A Monte Carlo formulation of the Bogolubov theory

We propose an efficient stochastic method to implement numerically the Bogo lubov approach to study finite-temperature Bose-Einstein condensates. Our m ethod is based on the Wigner representation of the density matrix describin g the non-condensed modes and a Brownian motion simulation to sample the Wi gner distribution at thermal equilibrium. Allowing it to sample any density operator Gaussian in the field variables, our method is very general and i t applies both to the Bogolubov and to the Hartree-Fock Bogolubov approach, in the equilibrium case as well as in the time-dependent case. We think th at our method can be useful to study trapped Bose-Einstein condensates in t wo or three spatial dimensions without rotational symmetry properties, as i n the case of condensates with vortices, where the traditional Bogolubov ap proach is difficult to implement numerically due to the need to diagonalize very big matrices.