  The investigation of the pair correlation statistics of sequences was
initially motivated by questions concerning quasi-energy-spectra of quantum
systems. However, the subject has been developed far beyond its roots in
mathematical physics, and many challenging number-theoretic questions on the
distribution of the pair correlations of certain sequences are still open. We
give a short introduction into the subject, recall some known results and open
problems, and in particular explain the recently established connection between
the distribution of pair correlations of sequences on the torus and certain
concepts from additive combinatorics. Furthermore, we slightly improve a result
recently given by Jean Bourgain.
