Macroscopic Suppression of Supersonic Quantum Transport

We consider a broad class of strongly interacting quantum lattice gases, including the Fermi-Hubbard and Bose-Hubbard models. We focus on macroscopic particle clusters of size θN, with θ∈(0,1) and N the total particle number, and we study the quantum probability that such a cluster is transported across a distance r within time t. Conventional effective light cone arguments yield a bound of the form exp(vt-r). We report a substantially stronger bound exp[θN(vt-r)], which provides exponential suppression that scales with system size. Our result establishes a universal dynamical large deviation principle: macroscopic suppression of supersonic macroscopic transport (MASSMAT).