Scattering theory of adiabatic reaction forces due to out-of-equilibrium quantum environments

The Landauer-Büttiker theory of mesoscopic conductors was recently extended to nanoelectromechanical systems. In this extension, the adiabatic reaction forces exerted by the electronic degrees of freedom on the mechanical modes were expressed in terms of the electronic $S$ matrix and its first nonadiabatic correction, the $A$ matrix. Here, we provide a more natural and efficient derivation of these results within the setting and solely with the methods of scattering theory. Our derivation is based on a generic model of a slow classical degree of freedom coupled to a quantum-mechanical scattering system, extending previous work on adiabatic reaction forces for closed quantum systems.

Figure 1

Example of a scattering system that is coupled to slow classical degrees of freedom $\mathbf{X}\left(t\right)$. The movement of the scatterer changes the scattering potential $V\left[\mathbf{X}\right(t\left)\right]$. The backaction of the electrons passing through the scatterer then leads to reaction forces acting on $\mathbf{X}\left(t\right)$.