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 the 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.

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• Ballistic transport
• Coulomb blockade
• Edge states
• Mesoscopics
• Quantum Hall effect
• Quantum transport
• Two-dimensional electron gas