  Phase-space methods allow one to go beyond the mean-field approximation to
simulate the quantum dynamics of interacting fields. Here, we obtain a
technique for initializing either Wigner or positive-P phase-space simulations
of Bose-Einstein condensates with quantum states at a finite temperature. As a
means to calculate the initial states, we introduce the idea of a nonlinear
chemical potential, which removes the zero-momentum phase-noise divergences of
Bogoliubov theory to give a diagonal Hamiltonian. The resulting steady-state
quantum theory is then directly applicable to the calculations of initial
conditions for quantum simulations of BEC dynamics using phase-space
techniques. These methods allow efficient and scalable simulation of large
Bose-Einstein condensates. We suggest that nonlinear chemical potentials may
have a general applicability to cases of broken symmetry.
