Thermalization with Gaussian Quantum Cellular Automata

arXiv:2606.05542v2 Announce Type: replace-cross Abstract: We study the long-time dynamics of many-body bosonic lattice systems under translation-invariant Gaussian quantum cellular automata. We formulate two sets of conditions on GQCAs which separately guarantee thermalization of any state on the local Weyl algebra to the infinite temperature state, whenever the state is locally normal and has uniformly bounded particle density. Our main intermediate result is a quantum many-body generalization of the classic Riemann-Lebesgue lemma which is a bound on expectation values of local Weyl operators involving their support and the state's particle density.