Vasseur, RomainSingh, Hansveer2025-01-242025-01-242024-0910.7275/55392https://hdl.handle.net/20.500.14394/55392Despite quantum mechanics being an established theory for just over a century, much of our understanding of the dynamics of macroscopic quantum systems has only emerged in the past thirty years, largely due to the advent of noisy intermediate-scale quantum devices. This thesis focuses on the universal phenomena that arise in the far-from-equilibrium dynamics of macroscopic quantum systems. In the first part of this thesis, we explore emergent hydrodynamics in minimally structured models known as random unitary circuits. Despite their differences from conventional Hamiltonian time evolution, random unitary circuits capture universal features of non-equilibrium quantum dynamics. We use these circuits to examine the effects of kinetic constraints on hydrodynamics and construct a family of random unitary circuits that exhibit Navier-Stokes hydrodynamics, despite lacking continuous translation invariance. Next, we investigate the hydrodynamics of integrable spin chains, characterized by an extensive number of extensive conserved quantities and stable ballistically propa- vi gating quasiparticles. Despite the presence of ballistically propagating quasiparticles, transport does not need to be ballistic. We demonstrate that initial state fluctuations in these conserved quantities significantly influence universal hydrodynamic behavior and are the source of non-ballistic transport. Furthermore, we construct a reversible quantum cellular automaton that showcases the exotic dynamical behaviors observ- able in integrable systems, specifically illustrating that this automaton is a discrete time crystal. Finally, we discuss a class of macroscopic one-dimensional systems that fail to thermally equilibrate due to the presence of disorder, a phenomenon known as many- body localization. We specifically investigate the phase transition between thermaliz- ing and many-body localizing behavior in the presence of quasiperiodic disorder. By studying the properties of local integrals of motion characteristic of the many-body localized phase, we extract properties of the critical point using finite-size scaling. Our results suggest that this transition shares features with many-body localization originating from uncorrelated random disorder.Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/physicsnonequilibriumdynamicsquantumhydrodynamicsDissertation (Open Access)https://orcid.org/0000-0002-8309-7711