Classical Dynamics Generated by Long-Range Interactions for Lattice Fermions and Quantum Spins

• URL: http://arxiv.org/abs/2009.05315v1
• Date: Fri, 11 Sep 2020 10:00:12 GMT
• Title: Classical Dynamics Generated by Long-Range Interactions for Lattice Fermions and Quantum Spins
• Authors: J.-B. Bru and W. de Siqueira Pedra
• Abstract summary: We study the macroscopic dynamical properties of fermion and quantum-spin systems with long-range, or mean-field, interactions. As is usual, the classical dynamics is driven by Liouville's equation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the macroscopic dynamical properties of fermion and quantum-spin systems with long-range, or mean-field, interactions. The results obtained are far beyond previous ones and require the development of a mathematical framework to accommodate the macroscopic long-range dynamics, which corresponds to an intricate combination of classical and short-range quantum dynamics. In this paper we focus on the classical part of the long-range, or mean-field, macroscopic dynamics, but we already introduce the full framework. The quantum part of the macroscopic dynamics is studied in a subsequent paper. We show that the classical part of the macroscopic dynamics results from self-consistency equations within the (quantum) state space. As is usual, the classical dynamics is driven by Liouville's equation.

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