Numerical investigation of spatial inhomogeneities in gravity and quantum field theory

Many interesting phenomena, such as high-temperature superconductivity and the quark-gluon plasma, still lack a satisfyingly predictive theoretical description. However, recent advances have revealed a curious connection between quantum field theories at strong coupling and classical gravity. This correspondence, known as the gauge/gravity duality or holographic correspondence, offers a promising perspective for investigating strongly correlated systems. In this thesis, we focus on using these new tools to examine the consequences of breaking translational invariance in such systems. We first use this duality to study the holographic realization of a spatially inhomogeneous condensed matter device known as a Josephson junction. We do so by constructing the gravitational equivalent of two superconductors separated by a weak metallic link, from which we then extract various field-theoretic quantities of interest. These include the spontaneously generated Josephson current, the superconducting order parameter, as well as a novel quantity we refer to as edge currents, which are indicative of gapless chiral modes localized at the interfaces between phases. We then investigate the more abstract construct of entanglement entropy in holographic theories. We model the fast local injection of energy in a 2+1 dimensional field theory and study the resulting thermalization of quantum entanglement. We achieve this objective by numerically evolving the geometry dual to a local quench from which we then compute the area of various minimal surfaces, the holographic proxy for entanglement entropy. We observe the appearance of a lightcone featuring two distinct regimes of entanglement propagation and provide a phenomenological explanation of the underlying mechanisms at play. Finally, we turn our attention to spatial inhomogeneities in gravitational systems themselves. We use an approximation of general relativity in which the number of spacetime dimensions is infinite to investigate the Gregory-Laflamme instability of higher-dimensional charged black branes. We argue that charged branes are always unstable in this new language, and push the approximation to next-to-leading order to compute the critical dimension below which the instability results in horizon fragmentation. We also examine the stability properties of two-dimensional black membranes and find that the triangular lattice minimizes brane enthalpy.Science, Faculty ofPhysics and Astronomy, Department ofGraduat