Models for Quantum Measurement of Particles with Higher Spin

Abstract

The Curie–Weiss model for quantum measurement describes the dynamical measurement of a spin-12 by an apparatus consisting of an Ising magnet of many spins 12 coupled to a thermal phonon bath. To measure the z-component s=−l,−l+1,⋯,l of a spin l, a class of models is designed along the same lines, which involve 2l order parameters. As required for unbiased measurement, the Hamiltonian of the magnet, its entropy and the interaction Hamiltonian possess an invariance under the permutation s→s+1 mod 2l+1. The theory is worked out for the spin-1 case, where the thermodynamics is analyzed in detail, and, for spins 32,2,52, the thermodynamics and the invariance are presented.

Keywords

• quantum measurement
• Hamiltonian
• spin