Analogy of RKKY oscillations to the heat exchange in cold atoms

An oscillatory term is found in both the energy expectation and dynamics of a wave-packet in a time-varying harmonic trap and infinite potential well. They are proved to oscillate in coherence with the time lapse within each period depending on both the cutoff in transition energies and the specific route via which the potential is being varied. This oscillatory term is general to arbitrary potential forms since it derives from the interference between crossed transition trajectories. Close analogy is made to the Ruderman-Kittel-Kasuya-Yosida interaction for giant-magnetoresistance trilayers, where many-body quantum interference among scattering states renders the oscillation as a function of spacer width. This connection reveals the generality of quantum friction due to parasitic oscillations.