Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 493, Issue 1, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2020.124517
Keywords
Interacting fermions; Self-consistency equations; Quantum-spin; Classical and quantum dynamics; Extended quantum mechanics
Categories
Funding
- CNPq [308337/2017-4]
- FAPESP [2017/22340-9]
- Basque Government [IT641-13]
- BERC 2018-2021 program
- Spanish Ministry of Science, Innovation and Universities: BCAM Severo Ochoa accreditation [SEV-2017-0718, MTM2017-82160C2-2-P]
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The study focuses on the quantum part of the macroscopic dynamics with long-range interactions in fermion and quantum-spin systems, revealing a complex combination of classical and short-range quantum dynamics. The development of a suitable mathematical framework is necessary to go beyond previous results. The entanglement between classical and quantum worlds is attributed to the highly non local character of long-range interactions.
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.
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