{"paper":{"title":"Aging Wiener-Khinchin Theorem and Critical Exponents of $1/f$ Noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"A. Dechant, E. Barkai, E. Lutz, N. Leibovich","submitted_at":"2016-03-17T11:56:43Z","abstract_excerpt":"The power spectrum of a stationary process may be calculated in terms of the autocorrelation function using the Wiener-Khinchin theorem. We here generalize the Wiener-Khinchin theorem for nonstationary processes and introduce a time-dependent power spectrum $\\left\\langle S_{t_m}(\\omega)\\right\\rangle$ where $t_m$ is the measurement time. For processes with an aging correlation function of the form $\\left\\langle I(t)I(t+\\tau)\\right\\rangle=t^{\\Upsilon}\\phi_{\\rm EA}(\\tau/t)$, where $\\phi_{\\rm EA}(x)$ is a nonanalytic function when $x$ is small, we find aging $1/f$ noise. Aging $1/f$ noise is chara"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05440","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}