{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"1ed69ba4c04df36e2b0311001859c86342f3b5256792a9e8edbe5f65b140b77c","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b","dc48db54751644a4b489cac4f7984f838ea0d878538ad9c93f9a62cc569827ef"],"salt":"ef738c76f5315964739644e009e2c65acb533d06a3248db2a9ce9cfbc619aac6","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"mechanism","assisted_by":[],"external_id":"cm.amorphous-low-temperature.universal-tunneling-strength","kind":"phenomenon","literature_status":"open","n":"2","parents":[],"plain":"In every glass tested, sound waves lose nearly the same small fraction of their energy per cycle at low temperature, within a factor of about twenty. The standard tunneling model fits this but gives no reason why the number should be universal.","posed_since":"","precise":"Below $\\sim 1\\,\\mathrm{K}$ amorphous solids show specific heat $C \\sim T$, thermal conductivity $\\kappa \\sim T^{2}$ and an internal-friction plateau $Q^{-1} = (\\pi/2) C_{\\mathrm{tun}}$, with tunneling strength $C_{\\mathrm{tun}} = P \\gamma^{2}/(\\rho v^{2})$ between $\\sim 10^{-4}$ and $10^{-3}$ across chemically different glasses ($P$ = density of states of tunneling two-level systems, $\\gamma$ = deformation potential, $\\rho$ = mass density, $v$ = sound velocity); equivalently the phonon mean free path is $\\sim 150$ wavelengths. Explain this universality, e.g. by interaction-induced renormalization of the defects (Yu and Leggett; Burin and Kagan) or by a generic soft-mode mechanism, and predict where it fails.","problem_ref":"dc48db54751644a4b489cac4f7984f838ea0d878538ad9c93f9a62cc569827ef","references":"","settled_by":"A theory deriving $C_{\\mathrm{tun}} \\sim 10^{-4} \\text{ to } 10^{-3}$ from generic properties of glasses, confirmed by a predicted exception or by simulations that compute $P$ and $\\gamma$ in several model glasses.","status_note":"","title":"Why is sound absorption by tunneling defects the same in all 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