An exact stochastic field method for the interacting Bose gas at thermal equilibrium

We present a new exact method to numerically compute the thermodynamical properties of an interacting Bose gas in the canonical ensemble. As in our previous paper (Carusotto I, Castin Y and Dalibard J 2001 Phys. Rev. A 63 023606), we write the density operator ρ as an average of Hartree dyadics | N :ϕ 1 ⟩⟨ N :ϕ 2 | and we find stochastic evolution equations for the wavefunctions ϕ 1,2 such that the exact imaginary-time evolution of ρ is recovered after averaging over noise. In this way, the thermal equilibrium density operator can be obtained for any temperature T . The method is then applied to study the thermodynamical properties of a homogeneous one-dimensional N -boson system: although Bose-Einstein condensation cannot occur in the thermodynamical limit, a macroscopic occupation of the lowest mode of a finite system is observed at sufficiently low temperatures. If k B T >>µ, the main effect of interactions is to suppress density fluctuations and to reduce their correlation length. Different effects such as a spatial antibunching of the atoms are predicted for the opposite k B T ⩽µ regime. Our exact stochastic calculations have been compared with existing approximate theories.