Abstract
In this paper, we present a non-equilibrium quantum theory for transient electron dynamics in nanodevices based on the Feynman–Vernon influence functional. Applying the exact master equation for nanodevices we recently developed to the more general case in which all the constituents of a device vary in time in response to time-dependent external voltages, we obtained non-perturbatively the transient quantum transport theory in terms of the reduced density matrix. The theory enables us to study transient quantum transport in nanostructures with back-reaction effects from the contacts, with non-Markovian dissipation and decoherence being fully taken into account. For a simple illustration, we apply the theory to a single-electron transistor subjected to ac bias voltages. The non-Markovian memory structure and the nonlinear response functions describing transient electron transport are obtained.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. How electrons in nanostructures vary in time in response to time-dependent external fields is described by electron transient dynamics far from equilibrium. Such nonequilibrium dynamics are explained by the temporal evolution of a device from some specific initial preparation toward any designed state within an extremely short time. Attention to transient phenomena in nanodevices has concentrated principally on the problem of how quickly or slowly a device can turn a current on or off, but the big challenge is to understand and predict how reliably and efficiently a device can manipulate the quantum coherence of electron states through external bias and gate voltage controls. In this paper we develop a nonequilibrium theory in terms of an exact master equation which is capable of addressing these fundamental issues.
Main results. The master equation directly describes the time evolution of quantum states in an open system. The back-action from the environment induces dissipation and noise and leads to the loss of the quantum coherence (decoherence) of the system, as a non-Markovian memory effect associated with the historical state. We derive the exact master equation from the Feynman–Vernon influence functional approach in which the back-action memory effect is taken fully into account. The resulting master equation has a convolutionless form, so the non-Markovian memory dynamics is fully encoded in its time-dependent coefficients, which contain all the information in terms of the nonequilibirum Green functions. The transient transport phenomena and electron quantum state of nanodevices can be obtained from the master equation in a rather simple way, and the results depend explicitly on the initial state of devices. Therefore, the nonequilibrium electron transient dynamics in nanodevices can be fully addressed.
Wider implications. Electron transient dynamics far away from equilibrium in various nanodevices has attracted much attention recently, due to potential applications in nanotechnology and quantum information processing. Our work provides a fundamental theory for understanding the temporal behavior of quantum devices, as well as for establishing a quantum theory for feedback controls. It may also be helpful in understanding transient phenomena in biological systems, where quantum coherence and the non-Markovian memory effect should play an important role.