Bulk Heating Effects as Tests for Collapse Models

We discuss limits on the noise strength parameter in mass-proportional-coupled wave function collapse models implied by bulk heating effects, and examine the role of the noise power spectrum in comparing experiments of different types. This comparison utilizes a calculation of the rate of heating through phonon excitation implied by a general noise power spectrum $\lambda(\omega)$. We find that in the standard heating formula, the reduction 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 bulk heating rate is sharply reduced, allowing compatibility of current experimental results. We suggest possible new bulk heating experiments that can be performed subject to limits placed by natural heating from radioactivity and cosmic rays. The proposed experiments exploit the vanishing of thermal transport in the low temperature limit.