Abstract
In this Ph.D. thesis dissertation concerns the quantum dynamics of strongly-correlated quantum systems in out-of-equilibrium states. The research is neither restricted to static properties or long-term relaxation evolutions nor does it neglect effects on any relevant subsystem as is frequently done with the environment in master equations approaches. The focus of this work is to explore different quantum systems during several regimes of operations, then discover results that might be of interest to quantum control, and hence to quantum computation and quantum information processing. Our main results can be summarized as follows in three parts: Signature of Critical Dynamics, Driven Dicke Model as a Test-bed of Ultra-Strong Coupling, and Beyond the Kibble-Zurek Mechanism.
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