Analytic aspects of analogue Hawking radiation in Bose-Einstein condensates

We present a theoretical study of analogue Hawking effect in stepwise models of Bose-Einstein condensates. We focus on subsonic-supersonic configuration, where two stationary homogeneous condensates are connected by a step-like discontinuity in the local speed of sound. We provide a detailed analysis of the scattering processes of fluctuation modes at the sonic horizon based on microscopic Bogoliubov theory of dilute BECs. Spontaneous phonon emission is predicted to occur at the horizon as a conversion of vacuum fluctuations into on-shell real particles. The condensed-matter analogue of Hawking radiation arises as a thermal Bose spectrum to low frequency order in the subsonic region. Stepwise BEC configurations with an extended sonic region are also taken into account in order to address more general and realistic velocity flow profiles.