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

Kavli Affiliate: Michael Roukes
| Summary:
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 $h_-1,V_varepsilon equiv σ_A ^2, V_varepsilon/(2ln 2)$ independent of device size across 13 decades; volume-independent noise is excluded by 9$σ$, site-averaging by 3.8$σ$. 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 $|δm| propto sqrth_-1,V_varepsilon cdot V$.
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