  We study the sensitivity of coupled condensate formation dynamics on the
history of initial stochastic domain formation in the context of
instantaneously quenched elongated harmonically-trapped immiscible
two-component atomic Bose gases. The spontaneous generation of defects in the
fastest condensing component, and subsequent coarse-graining dynamics, can lead
to a deep oscillating microtrap into which the other component condenses,
thereby establishing a long-lived composite defect in the form of a dark-bright
solitary wave. We numerically map out diverse key aspects of these competing
growth dynamics, focussing on the role of shot-to-shot fluctuations and global
parameter changes (initial state choices, quench parameters and condensate
growth rates). We conclude that phase-separated structures observable on
experimental timescales are likely to be metastable states whose form is
influenced by the stability and dynamics of the spontaneously-emerging
dark-bright solitary wave.
