Emergent energy scales in magnonic systems with relative motion

Relative motion between interacting systems can generate emergent energy scales that are absent in isolated systems. While uniform motion can be eliminated by a Galilean transformation, relative motion between interacting systems generally cannot. In the presence of characteristic spatial structures, relative motion gives rise to a Doppler frequency scale determined by the characteristic wavevector of the excitation and the relative velocity of the system. This emergent scale provides a fundamental mechanism for driving nonequilibrium phenomena in moving systems. In particular, the emergent energy scale is determined by how the relative motion probes the spatial structure of the relevant excitation. In this tutorial, we illustrate these ideas using magnonic systems as a concrete platform. We first discuss motion-induced magnon transport between relatively moving ferromagnets, in which the Doppler frequency serves as an effective nonequilibrium bias in the perturbative regime. This mechanism produces magnon currents even in the absence of conventional driving forces such as temperature gradients or chemical potential differences. We then introduce motion-induced parametric instabilities. When the emergent scale becomes sufficiently large to resonantly create magnon pairs, the perturbative description breaks down, and the magnonic vacuum becomes unstable. Above a critical velocity threshold, spontaneous magnon-pair creation emerges, resulting in strongly enhanced transport and nonequilibrium dynamics. Connections to related phenomena, including quantum friction, Cherenkov emission, and Zeldovich superradiance, are also highlighted. The concept of an emergent energy scale provides a unifying framework for understanding transport phenomena and instabilities in quantum systems with relative motion.