Models for quantum measurement of particles with higher spin

• URL: http://arxiv.org/abs/2303.03831v1
• Date: Tue, 7 Mar 2023 11:57:11 GMT
• Title: Models for quantum measurement of particles with higher spin
• Authors: Theodorus Maria Nieuwenhuizen
• Abstract summary: The Curie-Weiss model for quantum measurement describes the measurement of a spin-$frac12$ by an apparatus consisting of an Ising magnet of many spins. The Hamiltonian of the magnet, its entropy and the interaction Hamiltonian possess an invariance under the permutation $sto s+1$ mod $2l+1$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: The Curie-Weiss model for quantum measurement describes the dynamical measurement of a spin-$\frac{1}{2}$ by an apparatus consisting of an Ising magnet of many spins $\frac{1}{2}$ coupled to a thermal phonon bath. To measure the $z$-component $s=-l,-l+1,\cdots,l$ 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 $s\to s+1$ mod $2l+1$. The theory is worked out for the spin-1 case, where the thermodynamics is analyzed in detail, and for spins $\frac{3}{2},2,\frac{5}{2}$ the thermodynamics and the invariance is presented.

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