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We investigate the properties of the molecular quantum dot(Holstein-Anderson) model using numerical and analytical techniques. Pathintegral Monte Carlo simulations for the cumulants of the distribution functionof the phonon coordinate reveal that at intermediate temperatures the effectivepotential for the oscillator exhibits two minima rather than a single one,which can be understood as a signature of a bistability effect. Astraightforward adiabatic approximation turns out to adequately describe theproperties of the system in this regime. Upon lowering the temperature the twopotential energy minima of the oscillator merge to a single one at theequilibrium position of the uncoupled system. Using the parallels to the X-rayedge problem in metals we derive the oscillator partition function. It turnsout to be identical to that of the Kondo model, which is known to possess auniversal low energy fixed point characterized by a single parameter -- theKondo temperature $T_K$. We derive an analog of $T_K$ for the molecular quantumdot model, present numerical evidence pointing towards the appearance of theKondo physics and discuss experimental implications of the discoveredphenomena.

Kondo effect and the fate of bistability in molecular quantum dots with strong electron-phonon coupling