On Thermodynamics of Driven Quantum Systems: Novel Results and Perspectives

Driven quantum systems are systems in which a set of parameters obeys a time-dependent protocol, both periodic and non-periodic. The study of these systems bridges theoretical advances with experimental realizations in a variety of platforms—these range from quantum dot arrays to molecular junctions to trapped ions. The theoretical study is challenging due to the inherent non-equilibrium nature of the problem. These systems offer an interesting playground for quantum thermodynamics. They can be studied as quantum machines, such as refrigerators, heat pumps or engines. This poses the challenge of redefining the laws of thermodynamics in the quantum realm. This effort implies taking into account the presence of coherence, entanglement and strong correlations with the environment. In this conceptual framework, we attempt to shed new light on specific setups with applications in quantum metrology. In the first part of the Thesis, we present novel results on the thermodynamics and transport properties of quantum dots. After thoroughly introducing the main methods, namely non-equilibrium Green's functions and scattering matrix techniques, we apply these tools to adiabatic charge pumping. In this context, quantum dots, subjected to external periodic driving, act as nano-mechanical engines, transferring charge from a source to a drain. We investigate the conditions under which the pumped charge becomes quantized and how thermodynamic quantities behave in this regime. Next, we will focus on the charge shuttle mechanism in movable quantum dots as an example of a quantum clock. This physical model describes transport through a molecular state bound to two leads by van der Waals forces, with an electric field pushing the molecule from the source to the drain. The periodic oscillations arising from the system's dissipative limit cycle solution provide the basis for time measurement. We examine quantum noise primarily associated with the tunnelling process. In the second part, we propose a quantum clock that utilizes the free energy resources generated by coupling to a quantum battery, consisting of an integrable spin chain driven out of equilibrium by a quench in a chosen parameter. The operating conditions of the clock in the manifold of parameters are examined, leading to the requirement of the crossing of the critical point in the battery. The lifetime of the battery's resources is found to be extensive in its size, even when choosing a global coupling observable in the battery.