A theoretical approach to thermal noise caused by an inhomogeneously distributed loss -- Physical insight by the advanced modal expansion

TL;DR

This paper introduces an advanced modal expansion method that improves the calculation of thermal noise in systems with inhomogeneous loss, providing better physical understanding and aligning with experimental measurements.

Contribution

It presents a modified modal expansion technique that accounts for correlations between modes, enhancing the accuracy of thermal noise predictions in inhomogeneous systems.

Findings

The advanced modal expansion aligns with experimental thermal fluctuation measurements.

It reveals the physical origin of discrepancies in traditional models.

Correlations between resonant modes significantly affect thermal noise estimates.

Abstract

We modified the modal expansion, which is the traditional method used to calculate thermal noise. This advanced modal expansion provides physical insight about the discrepancy between the actual thermal noise caused by inhomogeneously distributed loss and the traditional modal expansion. This discrepancy comes from correlations between the thermal fluctuations of the resonant modes. The thermal noise spectra estimated by the advanced modal expansion are consistent with the results of measurements of thermal fluctuations caused by inhomogeneous losses.