  We study transport through a double quantum dot system in which each quantum
dot is coupled to a phonon mode. Such a system can be realized, e.g., using a
suspended carbon nanotube. We find that the interplay between strong
electron-phonon coupling and inter-dot tunneling can lead to a negative
differential conductance at bias voltages exceeding the phonon frequency.
Various transport properties are discussed, and we explain the physics of the
occurrence of negative differential conductance in this system.
