Non-equilibrium dynamics of many body quantum systems

Abstract: This thesis deals with the study of dynamical properties of out-of-equilibrium quantum systems. We introduce in particular a general class of Spin-Boson models, which describe for example light-matter interaction or dissipative phenomena. We contribute to the development of a stochastic approach to describe the spin dynamics in these models. In this context, the effect of the bosonic environment is encapsulated into additional stochastic degrees of freedom whose time-correlations are determined by spectral properties of the bosonic environment. We use this approach to study many-body phenomena such as the dissipative quantum phase transition induced by an ohmic bosonic environment. Synchronization phenomena as well as dissipative topological transitions are identified. We also progress in the study of arrays of interacting light-matter systems. These theoretical developments follow recent experimental achievements, which could ensure a quantitative study of these phenomena. This notably includes ultra-cold atoms, trapped ions and cavity and circuit electrodynamics setups. We finally investigate hybrid systems comprising electronic quantum dots coupled to electromagnetic resonators, which enable us to provide a spectroscopic analysis of many-body phenomena linked to the Kondo effect. We also introduce thermoelectric applications in these devices.