Semi-Classical Dynamics in Quantum Spin Systems

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.

16 pages

References in corpus (2)

• The classical limit of quantum theory
• Time Evolution of Spin Waves

Cited by in corpus (10)

• Operator Spreading in Quantum Maps
• Sensitivity to small perturbations in systems of large quantum spins
• A Lax Pair Structure for the Half-Wave Maps Equation
• Steering Magnetic Skyrmions with Nonequilibrium Green's Functions
• A remark on the mean-field dynamics of many-body bosonic systems with random interactions
• Thermodynamics of the spin square
• Thermodynamics of the classical spin triangle
• Invariant measures for integrable spin chains and integrable discrete NLS
• The Spectral Gap and Low-Energy Spectrum in Mean-Field Quantum Spin Systems
• The classical spin triangle as an integrable system