A thermal noise model for a branched system of harmonic oscillators

We have calculated the thermal noise of a branched system of oscillators through the normal mode representation. This model describes well the mechanical behavior of the last stage suspension system like in the Virgo interferometer and is consistent with the predictions coming from the fluctuation-dissipation theorem. Moreover, the developed formalism can be useful to infer informations on the mechanical quantities of the uncoupled elements of the suspension and on the suspension thermal noise predictions for a third generation gravitational interferometer like the Einstein Telescope (ET).