Emergence of classical behavior from the quantum spin

TL;DR

This paper demonstrates how classical behavior emerges from quantum spin systems through a coarse-graining process, showing that large quantum spins can replicate classical dynamics.

Contribution

It introduces a method to derive classical Hamiltonian dynamics from constrained quantum spin evolution via state coarse-graining.

Findings

Large quantum spins exhibit classical behavior under constrained evolution.

Coarse-graining quantum states into equivalence classes leads to classical state evolution.

Classical Hamiltonian systems can be derived from quantum spin models in the large spin limit.

Abstract

Classical Hamiltonian system of a point moving on a sphere of fixed radius is shown to emerge from the constrained evolution of quantum spin. The constrained quantum evolution corresponds to an appropriate coarse-graining of the quantum states into equivalence classes, and forces the equivalence classes to evolve as single units representing the classical states. The coarse-grained quantum spin with the constrained evolution in the limit of the large spin becomes indistinguishable from the classical system.