Time-dependent relaxation of charge and energy in electronic nanosystems

Abstract: The study of the dynamics of strongly confined, interacting open quantum systems has attracted great interest over the past years, due to potential applications in nanoelectronics, metrology as well as quantum information. Most recent experimental and theoretical research in this field has shifted attention towards electronic heat currents, recognizing their potential for practical purposes as well as for tests of fundamental theories, and also aiming to control the inevitable heat dissipation of any dynamically operated electronic device. Using the generalized master equation framework and a novel second quantization approach in Liouville space, the research articles discussed in this thesis contribute to the theory of dynamics in electronic nanosystems in two related ways. On the one hand, we study the voltage-switch induced transient electronic charge and heat current out of a single-level quantum dot with strong local Coulomb interaction into a tunnel-coupled reservoir. The first paper discusses how to measure the decay rates governing the transient response of the quantum dot to the voltage switch; the second paper shows how the induced tunneling processes lead to energy dissipation, in time and in the presence of many-body charging effects. On the other hand, we identify a fundamental relation which represents a generalization of hermiticity for the effective Liouvillian governing the dissipative, nonunitary dynamics of a large class of tunnel-coupled, open fermionic quantum systems. Offering a more systematic way to characterize time-dependent decay, two initially surprising observations in the transient heat current out of the quantum dot studied in the papers turn out to be prime manifestations of this relation, and are shown to be of general nature: the existence of a decay rate that only depends on the coupling itself, and the signature of electron-electron attraction in the transient dynamics of systems with repulsive Coulomb interactions.