Many-body open quantum systems: from dynamics to thermodynamics

This thesis studies problems concerning the dynamics and thermodynamics of manybody quantum systems. We start by introducing the necessary theoretical concepts and tools forming the basis of this manuscript. The research presented can be split in two parts. The first one deals with the dynamics of many-body quantum systems subject to environmental dissipative effects of various forms, while the second one studies topics of thermodynamics in many-body quantum systems. The first part of the research presented studies the effects of an environment inducing dissipation. We establish and study the adiabatic dynamics of free-fermion models subject to a local Lindblad bath and in the presence of a time-dependent Hamiltonian. The merit of these models is that they can be solved exactly, which thus can help us to study the interplay between non-adiabatic transitions and dissipation in many-body quantum systems. After the adiabatic evolution, we evaluate the excess energy (average value of the Hamiltonian) as a measure of the deviation from reaching the target final ground state. We find a robust evidence of the fact that an optimal working time for the quantum annealing protocol emerges as a result of the competition between the non-adiabatic effects and the dissipative processes. We compare these results with matrix product operator simulations of an Ising system and show that the phenomenology we found applies also for this more realistic case. We then proceed to a scenario in which the environment is not detrimental, but is on the contrary the driving force of the effects studied. We demonstrate that persistent currents can be induced in a quantum system in contact with a structured reservoir, without the need of any applied gauge field. The working principle of the mechanism leading to their presence is based on the extension to the many-body scenario of non-reciprocal Lindblad dynamics. Specifically, we consider an interacting spin/boson model in a ring-shaped one-dimensional lattice coupled to an external bath. By employing a combination of cluster mean-field, exact diagonalization and matrix product operator techniques, we show that solely dissipative effects suffice to engineer steady states with a persistent current that survives in the limit of large systems. We also verify the robustness of such current in the presence of additional dissipative or Hamiltonian perturbation terms. The second part studies many-body quantum systems with a focus on thermodynamics. First, we investigate a quantum battery made of N two-level systems, which is charged by an optical mode via an energy-conserving interaction. We quantify the fraction of energy stored in the battery that can be extracted in order to perform thermodynamic work. We first demonstrate that this fraction is highly reduced by the presence of correlations between the charger and the battery or between the two-level systems composing the battery. We then show that the correlation-induced suppression of extractable energy, however, can be mitigated by preparing the charger in a coherent optical state. We conclude by proving that the charger-battery system is asymptotically free of such locking correlations in the N ! 1 limit. And lastly, we study open questions within the theory of open quantum systems. The Markovian evolution of an open quantum system is characterized by a positive entropy production, while the global entropy gets redistributed between the system and the environmental degrees of freedom. Starting from these premises, we analyse the entropy variation of an open quantum system in terms of two distinct relations: the Clausius inequality, that provides an intrinsic bound for the entropy variation in terms of the heat absorbed by the system, and an extrinsic inequality, which instead relates the former to the corresponding entropy increment of the environment. By modeling the thermalization process with a Markovian collisional model, we compare and discuss the two bounds, showing that the latter is asymptotically saturated in the limit of large interaction time. In this regime not only the reduced density matrix of the system reaches an equilibrium configuration, but it also factorizes from the environmental degrees of freedom.