J.-B. Bru and W. de Siqueira Pedra
Quantum Dynamics Generated by Long-Range Interactions for Lattice Fermions and Quantum Spins
(481K, pdf)

ABSTRACT.  We study the macroscopic dynamics of fermion and quantum-spin systems with long-range, or mean-field, interactions, which is 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. Its 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.