Super-radiant scattering of dispersive fields

Motivated by analogue models of classical and quantum field theory in curved spacetimes and their recent experimental realizations, we consider wave scattering processes of dispersive fields exhibiting two extra scattering channels. In particular, we investigate how standard super-radiant scattering processes are affected by subluminal or superluminal modifications of the dispersion relation. We analyse simple (1+1)-dimensional toy models based on fourth-order corrections to the standard second-order wave equation and show that low-frequency waves impinging on generic scattering potentials can be amplified during the process. In specific cases, by assuming a simple step potential, we determine quantitatively the deviations in the amplification spectrum that arise due to dispersion, and demonstrate that the amplification can be further enhanced due to the presence of extra scattering channels. We also consider dispersive scattering processes in which the medium where the scattering takes place is moving with respect to the observer and show that super-radiance can also be manifest in such situations.