Nonadiabatic Van der Pol oscillations in molecular transport

The force exerted by the electrons on the nuclei of a current-carrying molecular junction can be manipulated to engineer nanoscale mechanical systems. In the adiabatic regime a peculiarity of these forces is negative friction, responsible for Van der Pol oscillations of the nuclear coordinates. In this work we study the robustness of the Van der Pol oscillations against high-frequency bias and gate voltage. For this purpose we go beyond the adiabatic approximation and perform full Ehrenfest dynamics simulations. The numerical scheme implements a mixed quantum-classical algorithm for open systems and is capable to deal with arbitrary time-dependent driving fields. We find that the Van der Pol oscillations are extremely stable. The nonadiabatic electron dynamics distorts the trajectory in the momentum-coordinate phase space but preserves the limit cycles in an average sense. We further show that high-frequency fields change both the oscillation amplitudes and the average nuclear positions. By switching the fields off at different times one obtains cycles of different amplitudes which attain the limit cycle only after considerably long times.