Abstract
Coulomb interactions deeply affect quantum transport in simple ballistic systems, but their impact on scaled up ballistic structures remains underexplored. Here we theoretically consider a chain of small metallic dots with frozen charge dynamics, connected by ballistic channels. We identify a neutral mode of transport, that is specific to a chain with at least two islands, and entwines local diffusion by neutral excitations with long-range correlations between islands' charge states. We show, as an experimentally measurable signature of this many-body behavior, that the Wiedemann-Franz law is violated with a Lorenz ratio scaling as the square root of the chain's length.