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

  • M. L. Roukes
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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 ∝ 1/Vε. Surveying the published record, I find the invariant h−1 Vε ≡ σA 2 Vε/(2ln 2) independent of device size across 13 decades; volume-independent noise is excluded by 9σ, site-averaging by 3.8σ. 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| ∝ √(h−1 Vε · V).

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Cite

BibTeXRIS
BibTeX
@misc{roukes2026frequency,
  title = {{1/f frequency noise in mechanical resonators scales inversely with volume, not with quality factor}},
  author = {M. L. Roukes},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16668},
  eprint = {2609.16668},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16668},
}
RIS
TY  - UNPB
TI  - 1/f frequency noise in mechanical resonators scales inversely with volume, not with quality factor
AU  - M. L. Roukes
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.16668
UR  - https://arxiv.org/abs/2609.16668
AB  - 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 ∝ 1/V_ε. Surveying the published record, I find the invariant h_−1 V_ε ≡ σ_A ^2 V_ε/(2ln 2) independent of device size across 13 decades; volume-independent noise is excluded by 9σ, site-averaging by 3.8σ. 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| ∝ √(h_−1 V_ε · V).
ER  -