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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:493

Article

关键词: Interacting fermions;    Self-consistency equations;    Quantum-spin;    Classical dynamics;    Extended quantum mechanics;   

DOI  :  10.1016/j.jmaa.2020.124434

来源: Elsevier

【 摘 要 】

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. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free