  First principles simulations of the quantum dynamics of interacting Bose
gases using the stochastic gauge representation are analyzed. In a companion
paper, we showed how the positive P representation can be applied to these
problems using stochastic differential equations. That method, however, is
limited by increased sampling error as time evolves. Here, we show how the
sampling error can be greatly reduced and the simulation time significantly
extended using stochastic gauges. In particular, local stochastic gauges (a
subset) are investigated. Improvements are confirmed in numerical calculations
of single-, double-, and multi-mode systems in the weak mode coupling regime.
Convergence issues are investigated, including the recognition of two modes by
which stochastic equations produced by phase space methods in general can
diverge: movable singularities and a noise-weight relationship. The example
calculated here displays wave-like behaviour in spatial correlation functions
propagating in a uniform 1D gas after a sudden change in the coupling
constant.This could in principle be tested experimentally using Feshbach
resonance methods.
