Approximately Macroscopically Unique States and Quantum Mechanics

2025/10/26 by Lin, Huaxin, Wang, Hang
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2510.22692

Abstract

We show that Mumford's Approximately Macroscopically Unique (AMU) states exist for quantum systems consisting of unbounded self-adjoint operators when the commutators are small. In particular, AMU states always exist in position and momentum systems when the Planck constant |ℏ| is sufficiently small. However, we show that these standard quantum mechanical systems are far away from classical mechanical (commutative) systems even when |ℏ|→ 0.

Citations

• Existence of Approximately Macroscopically Unique States
• Almost commuting self-adjoint operators and measurements
• Approximating macroscopic observables in quantum spin systems with commuting matrices

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• Existence of Approximately Macroscopically Unique States
• Quantum theory at the macroscopic scale
• On the nature of the quantum states of macroscopic systems
• Locality and the classical limit of quantum systems
• Applying quantum mechanics to macroscopic and mesoscopic systems