We show that in multimode mechanical systems, the amplification of the lowest mode and the damping of all the other modes can be realized simultaneously via nonlinear feedback. The feedback-induced dynamics of the multimode system is related to the formation of phonon condensation. The phonon statistics of the lowest mode are similar to those of a phonon laser. Finally, we show the coherence of the lowest mode can be improved by an order of magnitude.

We examine whether lagged corporate sustainable growth (Pre-CSG) helps explain cross-firm differences in firm-specific risk responses as commodity futures market stress rises. Using Chinese commodity futures data, we construct a multidimensional Commodity Futures Market Stress Index (CFMSI) and relate it to Pre-CSG and firm-specific risk for Chinese A-share manufacturing firms. We find that firms with higher Pre-CSG exhibit weaker relative firm-specific risk responses as CFMSI rises, with the strongest evidence for downside idiosyncratic volatility. The economic magnitude is small: a one-standard-deviation increase in CFMSI combined with a one-standard-deviation difference in Pre-CSG corresponds to approximately a 0.056-percentage-point reduction in the annualized Downside IVOL differential, or about 0.25% of its sample mean. By contrast, Pre-CSG is not significantly associated with lower risk when CFMSI is around zero, the CFMSI reference-window mean, indicating a state-dependent rather than unconditional relation. The negative interaction is broadly preserved under alternative CFMSI constructions and additional predetermined firm controls, although statistical precision varies, and is further supported by alternative inference procedures and recursive future-stress timing tests. Complementary analyst evidence shows that the CFMSI × Pre-CSG Interaction Exposure is negatively associated with forecast disagreement in more restrictive specifications. In the baseline analyst-risk specification, greater disagreement is positively associated with firm-specific risk measured in the following calendar year; however, this association attenuates and loses statistical significance when disagreement is reconstructed using only forecasts issued before that risk window begins. Overall, our findings suggest that the relation between corporate sustainable growth and firm-specific risk varies with commodity futures market stress.