{
  "id": "0710.2710",
  "version": "v1",
  "published": "2007-10-15T03:13:28.000Z",
  "updated": "2007-10-15T03:13:28.000Z",
  "title": "Fluctuation-dissipation theorem for thermo-refractive noise",
  "authors": [
    "Yuri Levin"
  ],
  "comment": "3 pages",
  "doi": "10.1016/j.physleta.2007.11.007",
  "categories": [
    "cond-mat.stat-mech",
    "astro-ph",
    "gr-qc"
  ],
  "abstract": "We introduce a simple prescription for calculating the spectra of thermal fluctuations of temperature-dependent quantities of the form $\\hat{\\delta T}(t)=\\int d^3\\vec{r} \\delta T(\\vec{r},t) q(\\vec{r})$. Here $T(\\vec{r}, t)$ is the local temperature at location $\\vec{r}$ and time $t$, and $q(\\vec{r})$ is an arbitrary function. As an example of a possible application, we compute the spectrum of thermo-refractive coating noise in LIGO, and find a complete agreement with the previous calculation of Braginsky, Gorodetsky and Vyatchanin. Our method has computational advantage, especially for non-regular or non-symmetric geometries, and for the cases where $q(\\vec{r})$ is non-negligible in a significant fraction of the total volume.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-15T03:13:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fluctuation-dissipation theorem",
      "thermo-refractive noise",
      "total volume",
      "simple prescription",
      "significant fraction"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Physics Letters A",
      "year": 2008,
      "month": "Mar",
      "volume": 372,
      "number": 12,
      "pages": 1941
    },
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008PhLA..372.1941L"
    }
  }
}