The Superballistic Photon

Ballistic transport is supposed to be the ceiling. When the system is smaller than the mean free path of energy carriers, particles travel from one end to the other without scattering. Thermal conductivity scales linearly with system size: k ~ L. You can’t move energy faster than when nothing impedes it.

This paper predicts a superballistic regime where thermal conductivity scales as k ~ L^1.5 — faster than free propagation.

The system is a dilute chain of plasmonic nanoparticles inside an optical cavity. The cavity modes create long-range photonic couplings between nanoparticles that don’t exist in free space. In the ballistic limit, each nanoparticle radiates to its neighbors. In the superballistic regime, cavity-guided modes amplify correlations across the entire chain, so energy transfer at one end constructively enhances transfer at the other.

The superlinear scaling comes from the collective nature of cavity-mediated interactions. Unlike direct dipole-dipole coupling (which decays with distance), cavity modes couple all particles simultaneously. As the chain grows, the number of contributing cavity modes grows too, and the collective enhancement compounds. The conductivity doesn’t just keep pace with system size — it outpaces it.

The ballistic limit assumed that the fastest transport is the one with fewest scattering events. That’s true when interactions are local. When the cavity creates non-local correlations, the collective response is faster than any single carrier could be. The ceiling was never the speed of individual particles. It was the absence of long-range cooperation.