Exact Reformulation of the Bosonic Many-Body Problem in Terms of Stochastic Wave Functions: an Elementary Derivation

Recently, a new method was developed to reformulate in an exact way the N-body problem of interacting bosons in terms of the stochastic evolution of single particle wavefunctions, see I. Carusotto, Y. Castin, and J. Dalibard, Phys. Rev. A 63, 023606 (2001). The original derivation is however often considered as rather involved. For the specific scheme called ‘simple Fock scheme’ we present here a very elementary derivation of such an approach.