Classical Dynamics Generated by Long-Range Interactions for Lattice Fermions and Quantum Spins
arXiv:2009.05315 · doi:10.1016/j.jmaa.2020.124434
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.
In press
References in corpus (7)
- Mean field evolution of fermions with Coulomb interaction
- Lieb-Robinson Bounds for Multi-Commutators and Applications to Response Theory
- Non-cooperative Equilibria of Fermi Systems With Long Range Interactions
- Effect of a Locally Repulsive Interaction on s-wave Superconductors
- Derivation of the time dependent Gross-Pitaevskii equation for a class of non purely positive potentials
- Quantum Dynamics Generated by Long-Range Interactions for Lattice Fermions and Quantum Spins
- Long time behaviour of interacting particles through a vibrating medium: comparison between the N-particle systems and the natural kinetic equation dynamics