Non-equilibrium phenomena in nanostructured and low-dimensional correlated systems

The prospects of inducing and engineering novel properties in condensed-matter systems by external perturbation have stimulated a significant interest in the field of non-equilibrium condensed-matter physics, which also benefit from the recent experimental progress in the fabrication and control of nanostructures and low-dimensional materials. In this thesis, we study a selection of steady-state phenomena in interacting nanostructured and low-dimensional condensed-matter systems out of equilibrium within two main lines of research: I) quantum transport in two particular nanostructures engineered for thermoelectric and information science purposes, and II) periodically driven low-dimensional systems.
In the first part of the thesis we discuss two projects where electron currents between reservoirs with different electrochemical potentials drive the non-equilibrium behavior: i) interaction-mediated thermoelectric effects in Coulomb-coupled quantum dots, and ii) non-local transport properties of a Cooper pair splitter. In project i), we set up a master equation with rates calculated from the T matrix. This enables us to discuss the role of higher-order (cotunneling) processes in the general case of energy-dependent couplings to external leads. Both aspects (higher-order processes and energy-dependent couplings) become important in discussing the optimization of the interaction-mediated energy-exchange that enables a cooling-by-current behavior in the device. In project ii), we propose to characterize a Cooper pair splitter in terms of the distribution of electron waiting times between tunneling events, and we show how such transport statistics, including analytical results for the more conventional finite-frequency shot noise, can provide valuable insights into the transport processes. In the second part of the thesis, we study condensed-matter systems perturbed by periodically oscillating electric fields. We first consider the periodically driven non-interacting single level and square-lattice, where for the former we provide an explicit example of how the periodically driven system approaches a non-equilibrium steady state. Thereafter, we turn our attention to the Coulomb-interacting case in the two-dimensional square-lattice Hubbard model. Guided by our knowledge in equilibrium, we consider fluctuations around the antiferromagnetic mean field and discuss how properties of the system change with a periodic drive. We show examples of how the drive can induce dynamics in the antiferromagnetic mean field and tune the magnon velocity. We highlight the importance of collective-mode excitations which, as we show, in general have a non-thermal distribution, which in turn may destabilize antiferromagnetism. Finally, we outline a route for future studies, in particular by deriving analytical results for fluctuations in the periodically driven level, which we show provide valuable insights into the on-set of mean-field configurations also out of equilibrium.