Non-equilibrium dynamics of dissipative strongly-correlated quantum matter

Understanding relaxation in interacting quantum many-body systems is a central problem in modern physics. While isolated systems thermalize through internal quantum chaos, realistic systems are inevitably coupled to external environments, giving rise to open-system dynamics where dissipation and memory effects can strongly modify relaxation processes. This thesis investigates relaxation in open quantum many-body systems in both Markovian and non-Markovian regimes.

In the first part, we formulate and test a Lindbladian analogue of the eigenstate thermalization hypothesis (ETH), characterizing the statistical structure of observables in the eigenbasis of generic Liouvillian superoperators. Using numerical simulations of several chaotic models, we demonstrate the universality and robustness of this Lindbladian ETH ansatz, including in regimes where trace preservation is relaxed.

In the second part, we study a strongly correlated open Sachdev-Ye-Kitaev (SYK) model coupled to pseudogapped non-Markovian baths. Using the Keldysh formalism and large-N methods, we uncover a rich dynamical phase diagram featuring bath-driven algebraic relaxation, chaos-driven exponential relaxation, and intermediate crossover regimes. Additionally, we analyze the real-time thermalization dynamics of the model. By defining an effective temperature and a quantitative distance to thermal equilibrium, we identify clear signatures of prethermalization and Floquet heating saturation.

Together, these results provide a unified perspective on relaxation in open quantum many-body systems, clarifying both the universal structure of Markovian relaxation modes and the profound impact of non-Markovian environments on strongly correlated quantum dynamics.