Understanding Hawking radiation from simple models of atomic   Bose-Einstein condensates
  This chapter is an introduction to the Bogoliubov theory of dilute Bose condensates as applied to the study of the spontaneous emission of phonons in a stationary condensate flowing at supersonic speeds. This emission process is a condensed-matter analog of Hawking radiation from astrophysical black holes but is derived here from a microscopic quantum theory of the condensate without any use of the analogy with gravitational systems. To facilitate physical understanding of the basic concepts, a simple one-dimensional geometry with a stepwise homogenous flow is considered which allows for a fully analytical treatment. 
R. Balbinot, I. Carusotto, A. Fabbri, C. Mayoral, and A. Recati
gr-qc cond-mat.quant-gas hep-th