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arXiv · 1801.00509

Heating Through Phonon Excitation Implied by Collapse Models

Stephen L. Adler
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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.

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Stephen L. Adler. 2018-01-01. Heating Through Phonon Excitation Implied by Collapse Models. https://doi.org/10.1103/physreva.97.052119

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