  The nonequilibrium dynamics of molecular devices is studied in the framework
of a generic model for single-molecule transistors: a resonant level coupled by
displacement to a single vibrational mode. In the limit of a broad level and in
the vicinity of the resonance, the model can be controllably reduced to a form
quadratic in bosonic operators, which in turn is exactly solvable. The response
of the system to a broad class of sudden quenches and ac drives is thus
computed in a nonperturbative manner, providing an asymptotically exact
solution in the limit of weak electron-phonon coupling. From the analytic
solution we are able to (1) explicitly show that the system thermalizes
following a local quantum quench, (2) analyze in detail the time scales
involved, (3) show that the relaxation time in response to a quantum quench
depends on the observable in question, and (4) reveal how the amplitude of
long-time oscillations evolves as the frequency of an ac drive is tuned across
the resonance frequency. Explicit analytical expressions are given for all
physical quantities and all nonequilibrium scenarios under study.
