We explore electronic transport in a nanotube quantum dot strongly coupled with vibrations and weakly with leads and the thermal environment. We show that the recent observation of anomalous conductance signatures in single-walled carbon nanotube quantum dots [B. J. LeRoy , Nature (London) 395, 371 (2004) and B. J. LeRoy , Phys. Rev. B 72, 075413 (2005)] can be understood quantitatively in terms of current driven "hot phonons" that are strongly correlated with electrons. Using rate equations in the many-body configuration space for the joint electron-phonon distribution, we argue that the variations are indicative of strong electron-phonon coupling requiring an analysis beyond the traditional uncorrelated phonon-assisted transport (Tien-Gordon) approach.
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