Dynamics of open fermionic nano-systems -- a fundamental symmetry and its application to electron transport in interacting quantum dots

Doctoral thesis, 2018

The study of electronic transport through strongly confined, interacting open quantum systems has regained considerable interest over the past years. One main motivation behind this concerns the possibility of time-dependently controlled operations on individual electrons, promising applications in, e.g., metrology and electron-based quantum computing. In particular, fundamental questions of quantum thermodynamics and the practical necessity to recover waste heat from nanocircuits have attracted attention towards electronic energy currents.

The research articles covered by this thesis contribute to this topic by deriving and exploring a fundamental symmetry relation -- the fermionic duality. This duality applies to the quantum master equation of any locally interacting, fermionic open quantum system tunnel-coupled to non-interacting reservoirs. It yields a crosslink between modes and amplitudes corresponding to the evolution rates in the time-dependent decay of the open-system state. This crosslink involves a mapping between the system of interest and a dual system with inverted environment potentials, local energies, and thus especially inverted interactions. The duality thereby explains many, at first sight unintuitive, transport features and significantly improves their analytic accessability. In particular, we can understand why charge- and energy currents through quantum dots with strong local Coulomb repulsion in fact exhibit features of electron-electron attraction, both in the time-dependent decay after a sudden switch and in the stationary limit.

More fundamental insights are obtained by identifying the duality to be rooted in Pauli's exclusion principle and the parity superselection principle. Namely, this implies that the duality is independent of, and hence combinable with many other general symmetries, including particle-hole symmetry, time-reversal symmetry, detailed balance and Onsager reciprocity. Especially the combination with the latter offers a novel perspective on the thermoelectric response of open, locally interacting electronic nanosystems.