19-38 J.-B. Bru and W. de Siqueira Pedra
Quantum Dynamics Generated by Long-Range Interactions for Lattice Fermions and Quantum Spins (481K, pdf) Jun 14, 19
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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.

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