Transient dynamics of an adiabatic NEMS

TL;DR

This study investigates the transient behavior of an adiabatic NEMS with a nano-mechanical oscillator and quantum dot, revealing long characteristic times and the absence of hysteresis in the steady state.

Contribution

It provides a detailed numerical analysis of transient dynamics in a coupled NEMS system, highlighting the long timescales and stability properties.

Findings

System reaches a unique steady state regardless of initial conditions.

Transient times can be significantly longer than the oscillator period.

Long transient times are observable at low bias, relevant for experiments.

Abstract

This paper is focused on the transient dynamics of an adiabatic nano-electromechanical system (NEMS), consisting of a nano-mechanical oscillator coupled to a quantum dot. By numerically solving the nonlinear stochastic differential equation governing the oscillator, the time evolution of the oscillator position, of the dot occupation number and of the current are studied. Different parameter settings are studied where the system exhibits bi-stable, tri-stable or mono-stable behavior on a finite-time horizon. It is shown that, after a typically long transient, the system under investigation exhibits no hysteretic behavior and that a unique steady state is reached, independently of the initial conditions. The transient dynamics is marked out by one or two well separated characteristic times, depending on the considered case (i.e., mono- or multi-stable). We evaluate these times for a dot on-resonance or off-resonance. It turns out that the characteristic time scales are long in comparison to the period of the uncoupled oscillator, particularly at low bias, suggesting that the predicted transient dynamics may be observed in state-of-the-art experimental setups.