Semi-Classical Dynamics in Quantum Spin Systems

TL;DR

This paper investigates how quantum spin systems behave in large-spin and mean-field limits, showing their dynamics approximate classical Hamiltonian systems, with extensions to infinite systems and coherent states.

Contribution

It establishes an Egorov-type theorem connecting quantum and classical spin dynamics in large-scale and mean-field regimes, including thermodynamic limits.

Findings

Quantum spin dynamics converge to classical Hamiltonian dynamics in large-spin and mean-field limits.

Results extend to infinite lattice and continuum systems.

Time evolution of coherent states approximates classical behavior in these regimes.

Abstract

We consider two limiting regimes, the large-spin and the mean-field limit, for the dynamical evolution of quantum spin systems. We prove that, in these limits, the time evolution of a class of quantum spin systems is determined by a corresponding Hamiltonian dynamics of classical spins. This result can be viewed as a Egorov-type theorem. We extend our results to the thermodynamic limit of lattice spin systems and continuum domains of infinite size, and we study the time evolution of coherent spin states in these limiting regimes.