  We analyze various limits of vibrationally coupled resonant electron
transport in single-molecule junctions. Based on a master equation approach, we
discuss analytic and numerical results for junctions under a high bias voltage
or weak electronic-vibrational coupling. It is shown that in these limits the
vibrational excitation of the molecular bridge increases indefinitely, i.e. the
junction exhibits a vibrational instability. Moreover, our analysis provides
analytic results for the vibrational distribution function and reveals that
these vibrational instabilities are related to electron-hole pair creation
processes.
