| Abstract: |
| We study propagation properties of nonequilibrium lattice models with long-range bosonic interactions. We prove (A) microscopic particle transport bounds and (B) Lieb-Robinson bounds, which are all thermodynamically stable. For both (A) and (B), we require Bose-Hubbard type Hamiltonians with hopping matrix decaying as $|x-y|^{-\alpha}$, $\alpha>d+2$ and initial state with uniformly bounded density from above. For (B), we further assume initially no particle lies in the region separating the supports of the probing observables. The proofs are based on a combination of commutator method originated in scattering theory and novel monotonicity estimate for certain adiabatic observables that track the spacetime localization of evolving states. |
|