Minimal spin-rotor model for Barnett and Einstein--de Haas physics

• URL: http://arxiv.org/abs/2604.23768v1
• Date: Sun, 26 Apr 2026 15:41:34 GMT
• Title: Minimal spin-rotor model for Barnett and Einstein--de Haas physics
• Abstract summary: We show that the Barnett effective-field picture changes qualitatively once the mechanical degree of freedom itself is quantized.<n>Our results identify a minimal quantum setting in which the Barnett effective-field picture departs from its classical form.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Barnett effect is usually understood through an effective magnetic field generated by mechanical rotation, while its reciprocal Einstein--de Haas effect describes the transfer of spin angular momentum to mechanical motion. We show that this effective-field picture changes qualitatively once the mechanical degree of freedom itself is quantized. To demonstrate this, we introduce an exactly solvable minimal spin-rotor model in which a spin-$1/2$ is coupled to a quantum rotor. In a fixed angular-momentum sector, the model reproduces the conventional Barnett splitting and remains formally equivalent to a Zeeman problem. For a superposition of rotor sectors, however, the Barnett field becomes operator-valued and the resulting dynamics generates coherent spin-rotor entanglement. This is directly visible in the reduced spin purity, rotor coherence, and entanglement entropy. Our results identify a minimal quantum setting in which the Barnett effective-field picture departs from its classical form and acquires a reciprocal manifestation through spin-dependent rotor coherence.

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