Transport at Strong Coupling and Black Hole Dynamics

In this thesis we study aspects of transport in strongly coupled quantum systems with broken translational symmetry. Using holographic duality, we also examine the associated dynamical problem in asymptotically Anti-de Sitter, spatially modulated black holes. More precisely, in chapter 2 we consider the transport of conserved charges in spatially inhomogeneous quantum systems with a discrete lattice symmetry. When the DC conductivities are finite, we derive a set of generalised Einstein relations, relating the diffusion constants of the conserved charges to the DC conductivities and static susceptibilities. We also develop a long-wavelength expansion in order to explicitly construct the heat and charge diffusive modes within hydrodynamics on curved manifolds. In chapter 3 we used analogous techniques to construct the thermoelectric diffusive quasinormal modes in a large class of black hole spacetimes that are holographically dual to strongly coupled field theories in which spatial translations are broken explicitly. These modes satisfy a set of constraints on the black hole horizon, from which we find that their dispersion relations are given by the generalised Einstein relations. In chapter 4 we define a boost incoherent current in spontaneously modulated phases, and we show that in holographic theories, its DC conductivity can be obtained from solving a system of horizon Stokes equations.