  We present the first special relativistic, axisymmetric hydrodynamic
simulations of black hole-torus systems (approximating general relativistic
gravity) as remnants of binary-neutron star (NS-NS) and neutron star-black hole
(NS-BH) mergers, in which the viscously driven evolution of the accretion torus
is followed with self-consistent energy-dependent neutrino transport and the
interaction with the cloud of dynamical ejecta expelled during the NS-NS
merging is taken into account. The modeled torus masses, BH masses and spins,
and the ejecta masses, velocities, and spatial distributions are adopted from
relativistic merger simulations. We find that energy deposition by neutrino
annihilation can accelerate outflows with initially high Lorentz factors along
polar low-density funnels, but only in mergers with extremely low baryon
pollution in the polar regions. NS-BH mergers, where polar mass ejection during
the merging phase is absent, provide sufficiently baryon-poor environments to
enable neutrino-powered, ultrarelativistic jets with terminal Lorentz factors
above 100 and considerable dynamical collimation, favoring short gamma-ray
bursts (sGRBs), although their typical energies and durations might be too
small to explain the majority of events. In the case of NS-NS mergers, however,
neutrino emission of the accreting and viscously spreading torus is too short
and too weak to yield enough energy for the outflows to break out from the
surrounding ejecta shell as highly relativistic jets. We conclude that neutrino
annihilation alone cannot power sGRBs from NS-NS mergers.
