Classical Dynamics Generated by Long-Range Interactions for Lattice Fermions and Quantum Spins
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.
Cite
@article{arxiv.2009.05315,
title = {Classical Dynamics Generated by Long-Range Interactions for Lattice Fermions and Quantum Spins},
author = {J. -B. Bru and W. de Siqueira Pedra},
journal= {arXiv preprint arXiv:2009.05315},
year = {2020}
}
Comments
In press