  The evolution of main sequence binaries resided in the galactic centre is
influenced a lot by the central super massive black hole (SMBH). Due to this
perturbation, the stars in a dense environment are likely to experience mergers
or collisions through secular or non-secular interactions. In this work, we
study the dynamics of the stellar binaries at galactic center, perturbed by
another distant SMBH. Geometrically, such a four-body system is supposed to be
decomposed into the inner triple (SMBH-star-star) and the outer triple
(SMBH-stellar binary-SMBH). We survey the parameter space and determine the
criteria analytically for the stellar mergers and the tidal disruption events
(TDEs). For a relative distant and equal masses SMBH binary, the stars have
more opportunities to merge as a result from the Lidov-Kozai(LK) oscillations
in the inner triple. With a sample of tight stellar binaries, our numerical
experiments reveal that a significant fraction of the binaries, ~70 per cent,
experience merger eventually. Whereas the majority of the stellar TDEs are
likely to occur at a close periapses to the SMBH, induced by the outer Kozai
effect. The tidal disruptions are found numerically as many as ~10 per cent for
a close SMBH binary that is enhanced significantly than the one without the
external SMBH. These effects require the outer perturber to have an inclined
orbit (>=40 degree) relatively to the inner orbital plane and may lead to a
burst of the extremely astronomical events associated with the detection of the
SMBH binary.
