Domain size distribution in phase separating binary Bose--Einstein condensates is studied theoretically by numerically solving the Gross--Pitaevskii equations at zero temperature. We show that the size distribution in the domain patterns arising from the dynamic instability obeys a power law in a scaling regime according to the dynamic scaling analysis based on the percolation theory. The scaling behavior is kept during the relaxation development until the characteristic domain size becomes comparable to the linear size of the system, consistent with the dynamic scaling hypothesis of the phase-ordering kinetics. Our numerical experiments indicate the existence of a different scaling regime in the size distribution function, which can be caused by the so-called coreless vortices.
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