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Abstract

This dissertation investigates the emergence of collective phenomena and universal patterns in strongly correlated quantum many-body systems, both in and out of equilibrium. We propose an asymptotically free scalar field theory in four dimensions and solve the coupling renormalization group flow to the strongly coupled infrared using a large-N resummation based on a global tensor symmetry. This provides a rare example of a non-perturbatively controlled interacting theory in four dimensions. We then demonstrate the formation of stable droplets in bosonic atom-molecule systems near narrow Feshbach resonances, stabilized by coherent interconversion dynamics, enabling a controlled study of the crossover from few-body clusters to many-body phases. Far from equilibrium, we analyze the emergence of universal scaling associated with nonthermal attractors in quantum systems ranging from cold atoms to the quark-gluon plasma. We demonstrate dynamical self-stabilization via a universal scaling instability, despite unstable perturbations from interactions between emergent quasiparticle states. We explain how systems approach these attractors through power-law resummation in time, which was recently confirmed in a cold atom experiment, and extend this so-called prescaling to gauge-invariant observables in Yang-Mills theories. Finally, we propose and demonstrate the emergence of hydrodynamic excitations near nonthermal attractors, characterized by time-dependent transport coefficients like shear viscosity.