Heating Through Phonon Excitation Implied by Collapse Models

TL;DR

This paper calculates phonon-induced heating rates in collapse models, showing how non-white noise spectra can significantly reduce heating compared to white noise assumptions.

Contribution

It derives a general formula for phonon heating rates in collapse models with arbitrary noise spectra, extending previous white noise results.

Findings

Heating rate reduces with non-white noise spectra cutoff

Derived a formula linking noise spectrum to phonon heating rate

Showed that noise cutoff below phonon frequencies sharply decreases heating

Abstract

We calculate the rate of heating through phonon excitation implied by the noise postulated in mass-proportional-coupled collapse models, for a general noise power spectrum. For white noise with reduction rate $\lambda$, the phonon heating rate reduces to the standard formula, but for non-white noise with power spectrum $\lambda(\omega)$, the rate $\lambda$ is replaced by $\lambda_{\rm eff}=\frac{2}{3 \pi^{3/2}} \int d^3w e^{-\vec w^2} \vec w^2 \lambda(\omega_L(\vec w/r_c))$, with $\omega_L(\vec q)$ the longitudinal acoustic phonon frequency as a function of wave number $\vec q$, and with $r_C$ the noise correlation length. Hence if the noise power spectrum is cut off below $\omega_L(|\vec q| \sim r_c^{-1})$, the heating rate is sharply reduced.