Particle creation and entanglement in a dispersive model with step velocity profile

We investigate particle creation and entanglement structure in a dispersive model with subluminal dispersion relation. Assuming the step function spatial velocity profile of the background flow, mode functions for a massless scalar field are exactly obtained by the matching method. Power spectrums of created particles are calculated for the subsonic and the trans-sonic flow cases. For the trans-sonic case, the sonic horizon exists, and created particles show the Planckian distribution for the low frequency region, but the thermal property disappears for the high frequency region near the cutoff frequency introduced by the nonlinear dispersion. For the subsonic case, although the sonic horizon does not exist, the effective group velocity horizon appears due to the nonlinear dispersion for the high frequency region, and an approximate thermal property of the power spectrum arises. The relation between particle creation and entanglement between each mode is also discussed.