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Disordered hyperuniform many-particle systems have attracted considerablerecent attention. One important class of such systems is the classical groundstates of "stealthy potentials." The degree of order of such ground statesdepends on a tuning parameter. Previous studies have shown that theseground-state point configurations can be counterintuitively disordered,infinitely degenerate, and endowed with novel physical properties (e.g.,negative thermal expansion behavior). In this paper, we focus on the disorderedregime in which there is no long-range order, and control the degree ofshort-range order. We map these stealthy disordered hyperuniform pointconfigurations to two-phase media by circumscribing each point with a possiblyoverlapping sphere of a common radius $a$: the "particle" and "void" phases aretaken to be the space interior and exterior to the spheres, respectively. Westudy certain transport properties of these systems, including the effectivediffusion coefficient of point particles diffusing in the void phase as well asstatic and time-dependent characteristics associated with diffusion-controlledreactions. Besides these effective transport properties, we also investigateseveral related structural properties, including pore-size functions, quantizererror, an order metric, and percolation threshold. We show that thesetransport, geometrical and topological properties of our two-phase mediaderived from decorated stealthy ground states are distinctly different fromthose of equilibrium hard-sphere systems and spatially uncorrelated overlappingspheres.

Transport, Geometrical and Topological Properties of Stealthy Disordered Hyperuniform Two-Phase Systems