Randomly charged net-neutral dielectric slabs are shown to interact across afeatureless dielectric continuum with long-range electrostatic forces thatscale with the statistical variance of their quenched random chargedistribution and inversely with the distance between their bounding surfaces.By accounting for the whole spectrum of electromagnetic field fluctuations, weshow that this long-range disorder-generated interaction extends well into theretarded regime where higher-order Matsubara frequencies contributesignificantly. This occurs even for highly clean samples with only a traceamount of charge disorder and shows that disorder effects can be important downto the nano scale. As a result, the previously predicted non-monotonic behaviorfor the total force between dissimilar slabs as a function of their separationdistance is substantially modified by higher-order contributions, and in almostall cases of interest, we find that the equilibrium inter-surface separation isshifted to substantially larger values compared to predictions based solely onthe zero-frequency component. This suggests that the ensuing non-monotonicinteraction is more easily amenable to experimental detection. The presence ofcharge disorder in the intervening dielectric medium between the two slabs isshown to lead to an additional force that can be repulsive or attractivedepending on the system parameters and can, for instance, wash out thenon-monotonic behavior of the total force when the intervening slab contains asufficiently large amount of disorder charges.
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