1/f frequency noise in mechanical resonators scales inversely with volume, not with quality factor

Abstract:Mechanical frequency-shift sensors have never reached their fundamental thermomechanical or quantum limits. Every material, size, and transduction scheme yet examined yields a $1/f$ floor 1-3 orders higher, with a flicker-noise coefficient $h_{-1} \propto 1/V_{\varepsilon}$. Surveying the published record, I find the invariant $h_{-1}\,V_{\varepsilon} \equiv \sigma_A ^2\, V_{\varepsilon}/(2\ln 2)$ independent of device size across 13 decades; volume-independent noise is excluded by 9$\sigma$, site-averaging by 3.8$\sigma$. No $Q$ dependence appears: reported $Q^{-n}$ laws scale equivalently when $Q$ and volume co-vary; only volume scaling survives when they do not. Mass resolution follows as $|\delta m| \propto \sqrt{h_{-1}\,V_{\varepsilon} \cdot V}$.

Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)

arXiv:2609.16668 [cond-mat.mes-hall]

(or arXiv:2609.16668v1 [cond-mat.mes-hall] for this version)

https://doi.org/10.48550/arXiv.2609.16668 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

SM_v112_2026-09-14.pdf

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