Testing collapse models by a thermometer

Collapse models postulate that space is filled with a collapse noise field, inducing quantum Brownian motions, which are dominant during the measurement, thus causing collapse of the wave function. An important manifestation of the collapse noise field, if any, is thermal energy generation, thus disturbing the temperature profile of a system. The experimental investigation of a collapse-driven heating effect has provided, so far, the most promising test of collapse models against standard quantum theory. In this paper, we calculate the collapse-driven heat generation for a three-dimensional multi-atomic Bravais lattice by solving stochastic Heisenberg equations. We perform our calculation for the mass-proportional continuous spontaneous localization collapse model with nonwhite noise. We obtain the temperature distribution of a sphere under stationary-state and insulated surface conditions. However, the exact quantification of the collapse-driven heat-generation effect highly depends on the actual value of cutoff in the collapse noise spectrum.