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Abstract

Recent technological advances in ultra-cold atom experiments have triggered strong efforts to develop quantum simulators for solving fundamental questions in modern physics. Far-reaching applications range from quantum chemistry and condensed matter physics to high-energy physics, nuclear physics and cosmology, where the evolution of underlying quantum fields is often difficult to compute with classical simulations. This dissertation contributes to the field of quantum simulations for the complex out-of-equilibrium dynamics of gauge fields and the ultra-cold quantum gases realized in current experiments and their applications to gauge theories. First, we present a scalable scheme to engineer a one-dimensional lattice gauge theory using ultra-cold atoms in a large-scale Bose-Hubbard quantum simulator, which is demonstrated in an experiment. The implementation allows us to furthermore investigate the thermalization dynamics of the gauge theory. Secondly, a scalable cold-atom quantum simulator for gauge-field dynamics in two spatial dimensions is proposed. We investigate an experimental building block of the proposal, where the many-body problem is characterized using the fluctuations in the data. Finally, we present an equal-time approach to the real-time dynamics of quantum fields through the non-equilibrium effective action. Focusing on non-perturbative Bose fields, we derive kinetic equations to establish a link between effective theories and observables accessible with current technology.