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Adiabatic reaction forces in mesoscopic systems

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Nanoelectromechanical systems are characterized by an intimate connection between electronic and mechanical degrees of freedom. Due to the nanoscopic scale, current flowing through the system noticeably impacts the vibrational dynamics of the device, complementing the effect of the vibrational modes on the electronic dynamics. In this talk I describe our recently developed formalism, in which we employ the scattering matrix approach to quantum transport to describe the current-induced forces acting on the mechanical degrees of freedom of an out-of-equilibrium nanoelectromechanical system. These forces control the Langevin dynamics of the mechanical modes. Specifically, we derive expressions for the (typically nonconservative) mean force, for the (possibly negative) damping force, an effective “Lorentz” force which exists even for time reversal invariant systems, and the fluctuating Langevin force originating from Nyquist and shot noise of the current flow. In a more general setting, these forces can be interpreted as reaction forces acting over slow classical degrees of freedom coupled to a quantum-mechanical scattering system, and our results extend previous work on adiabatic reaction forces for closed quantum systems. I will also go over some very recent results in which we describe the decay of the Loschmidt Echo of the out-of-equilibrium quantum-mechanical scattering system, in terms of the fluctuations and dissipation of the system.

This talk is part of the Theory of Condensed Matter series.

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