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First principles simulations of the quantum dynamics of interacting Bosegases using the stochastic gauge representation are analyzed. In a companionpaper, we showed how the positive P representation can be applied to theseproblems using stochastic differential equations. That method, however, islimited by increased sampling error as time evolves. Here, we show how thesampling error can be greatly reduced and the simulation time significantlyextended using stochastic gauges. In particular, local stochastic gauges (asubset) are investigated. Improvements are confirmed in numerical calculationsof single-, double-, and multi-mode systems in the weak mode coupling regime.Convergence issues are investigated, including the recognition of two modes bywhich stochastic equations produced by phase space methods in general candiverge: movable singularities and a noise-weight relationship. The examplecalculated here displays wave-like behaviour in spatial correlation functionspropagating in a uniform 1D gas after a sudden change in the couplingconstant.This could in principle be tested experimentally using Feshbachresonance methods.Comment: 39 pages, 11 figures, 2 tables. Major revision, especially Section 6  (convergence issues) which is almost all new, and also introduction. Now in J  phys A forma

First-principles quantum dynamics in interacting Bose gases II: stochastic gauges