Quantum dynamics generated by long-range interactions for lattice fermions and quantum spins

We study the macroscopic dynamics of fermion and quantum-spin systems with long-range, or mean-field, interactions, which turns out to be equivalent to an intricate combination of classical and short-range quantum dynamics. In this paper we focus on the quantum part of the long-range macroscopic dynamics. The classical part is studied in a companion paper. Altogether, the results obtained are far beyond previous ones and required the development of a suitable mathematical framework. The entanglement of classical and quantum worlds is noteworthy, opening new theoretical perspectives, and is shown here to be a consequence of the highly non local character of long-range, or mean-field, interactions. (c) 2020 Elsevier Inc. All rights reserved.