Randomness in Dissipative and Chaotic Quantum Dynamics

This book studies the different roles of randomness in quantum systems. Noise is one of the key limitations in current quantum platforms because of decoherence, which typically destroys quantum information and makes it effectively classical. In this book rather than as an obstacle we leverage noise to help us model, understand, and engineer new behavior in quantum systems. The book introduces quantities to characterize the action of noise in these systems, as well as develop a theory which models the effect of noise in dissipation. A second problem studied in the thesis where randomness also comes into play is in explaining the behavior of chaotic quantum systems, where randomness serves as a definition of what it means for a quantum system to be chaotic. Within the framework of quantum chaos, the book studies the behavior of long-range spectral correlations and analyzes how they manifest in building indicators of quantum chaos such as the ramp of the Spectral Form Factor. All in all the book provides a deeper look into the role played by randomness in different quantum systems, introducing tools to characterize its effect as well as uncovering new phenomena induced by the presence of noise.