Abstract
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 θ N, 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(v t-r). We report a substantially stronger bound exp(θ N(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).