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This course explores the non-equilibrium dynamics of scalar fields, focusing on the stability of many-body quantum systems and their coherent time evolution. It delves into mechanisms like Many-body localization, Floquet MBL, Dynamical Freezing, and Hilbert Space Fragmentation, which are crucial for understanding novel phases of quantum matter in and out of equilibrium. The course aims to integrate concepts from Condensed Matter Physics, Statistical Mechanics, Quantum Field Theory, and Mathematics to address the stability issues in quantum systems and devices. The teaching method involves summarizing state-of-the-art concepts and tools, targeting senior PhD students, postdocs, and faculty members in related fields.
