Fluctuation-dissipation theorem for thermo-refractive noise

Abstract

We introduce a simple prescription for calculating the spectra of thermal fluctuations of temperature-dependent quantities of the form $\widehat{\delta T}(t)=\int d^3\vec{r}\delta T(\vec{r},t)q(\vec{r})$. 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.

3 pages

References in corpus (1)

• Titania-doped tantala/silica coatings for gravitational-wave detection

Cited by in corpus (1)

• Coating thermal noise of a finite-size cylindrical mirror