We study current-induced vibrational cooling, heating, and instability in a donor-acceptor rectifying molecular junction using a full counting statistics approach. In our model, electron-hole pair excitations are coupled to a given molecular vibrational mode which is either harmonic or highly anharmonic. This mode may be further coupled to a dissipative thermal environment. Adopting a master equation approach, we confirm the charge and heat exchange fluctuation theorem in the steady-state limit, for both harmonic and anharmonic models. Using simple analytical expressions, we calculate the charge current and several measures for the mode effective temperature. At low bias, we observe the effect of bias-induced cooling of the vibrational mode. At higher bias, the mode effective temperature is higher than the environmental temperature, yet the junction is stable. Beyond that, once the vibrational mode (bias-induced) excitation rate overcomes its relaxation rate, instability occurs. We identify regimes of instability as a function of voltage bias and coupling to an additional phononic thermal bath. Interestingly, we observe a reentrant behavior where an unstable junction can properly behave at a high enough bias. The mechanism for this behavior is discussed.

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We expand iterative numerically-exact influence functional path-integral tools and present a method capable of following the nonequilibrium time evolution of subsystems coupled to multiple bosonic and fermionic reservoirs simultaneously. Using this method, we study the real-time dynamics of charge transfer and vibrational mode excitation in an electron conducting molecular junction. We focus on nonequilibrium vibrational effects, particularly, the development of vibrational instability in a current-rectifying junction. Our simulations are performed by assuming large molecular vibrational anharmonicity (or low temperature). This allows us to truncate the molecular vibrational mode to include only a two-state system. Exact numerical results are compared to perturbative Master equation calculations demonstrating an excellent agreement in the weak electron-phonon coupling regime. Significant deviations take place only at strong coupling. Our simulations allow us to quantify the contribution of different transport mechanisms, coherent dynamics and inelastic transport, in the overall charge current. This is done by studying two model variants: The first admits inelastic electron transmission only, while the second one allows for both coherent and incoherent pathways.

Key words non-Markovian decay, power law decay, bound stateIt is known that quantum systems yield non-exponential (power law) decay on long time scales, associated with continuum threshold effects contributing to the survival probability for a prepared initial state. For an open quantum system consisting of a discrete state coupled to continuum, we study the case in which a discrete bound state of the full Hamiltonian approaches the energy continuum as the system parameters are varied. We find in this case that at least two regions exist yielding qualitatively different power law decay behaviors; we term these the long time 'near zone' and long time 'far zone.' In the near zone the survival probability falls off according to a t −1 power law, and in the far zone it falls off as t −3 . We show that the timescale TQ separating these two regions is inversely related to the gap between the discrete bound state energy and the continuum threshold. In the case that the bound state is absorbed into the continuum and vanishes, then the time scale TQ diverges and the survival probability follows the t −1 power law even on asymptotic scales. Conversely, one could study the case of an anti-bound state approaching the threshold before being ejected from the continuum to form a bound state. Again the t −1 power law dominates precisely at the point of ejection.