Far-from-equilibrium universality and dynamics of nonequilibrium quantum many-body systems

Far from equilibrium, quantum many-body systems can exhibit emergent structures and universal behaviour that require effective descriptions capturing their macroscopic dynamics. Such descriptions must identify the relevant degrees of freedom, emergent symmetries, and collective excitations that govern the long-time evolution of these systems. This thesis investigates how these features manifest in strongly correlated quantum field theories by extracting nonequilibrium symmetries and developing methods to characterise their universal scaling behaviour. First, the restoration of symmetries in isolated quantum systems is examined. By deriving Ward identities for correlation functions, a method for extracting symmetries from experimental and numerical data is established. Applying this framework to ultracold atomic gases, it is demonstrated that explicitly broken symmetries are effectively restored long before thermalisation. The approach is also used to define spontaneous symmetry breaking in a nonequilibrium system. Subsequently, the role of emergent quasiparticles and defect-driven dynamics is investigated in a single-component scalar field theory with a focus on their connection to nonthermal fixed points, which arise as attractor solutions with universal scaling behaviour. Through real-time lattice simulations, unequal-time correlation functions are extracted to identify the dominant infrared excitations, which are connected to Kelvin waves propagating along vortex lines. Beyond correlation functions, a geometric approach is introduced to study topological structures directly. Using tools from topological data analysis, robust, nonlocal observables are defined that capture the coarsening dynamics of topological defects. These observables exhibit a distinct scaling behaviour compared to traditional correlation functions, highlighting the multiscaling nature of universal dynamics near nonthermal fixed points. Furthermore, the thesis explores the emergence of universal scaling behaviour in relativistic scalar field theories using an approach that goes beyond scaling analyses. By explicitly solving a self-consistent equation derived from the two-particle irreducible effective action, nonthermal scaling solutions are extracted. The results indicate a stationary transport regime characterised by a universal quadratic scaling.