Bulk Heating Effects as Tests for Collapse Models

TL;DR

This paper analyzes how bulk heating measurements constrain collapse model noise parameters, emphasizing the importance of the noise power spectrum and proposing new experiments leveraging low-temperature thermal transport properties.

Contribution

It introduces a detailed calculation of bulk heating rates based on the noise power spectrum and suggests new experiments to improve constraints on collapse models.

Findings

Bulk heating rate depends on the noise power spectrum and phonon excitation.

Cutting off the noise spectrum below certain frequencies reduces heating, aligning with experimental limits.

Proposes low-temperature experiments exploiting vanishing thermal transport to test collapse models.

Abstract

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.