Phase-space representations of thermal Bose-Einstein condensates

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.