Strongly Interacting Quantum Dynamics

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The dynamics of interacting quantum systems is central to many fundamental questions in modern physics, including understanding the transport properties of strongly correlated materials and the role of entanglement and chaos in thermalizing quantum systems. Further, due to the holographic correspondence, the dynamics of strongly interacting quantum field theories is intimately connected to key aspects of black hole physics including Hawking's information paradox. Nevertheless, progress in addressing these questions has been severely limited by a lack of techniques to study quantum dynamics outside of weakly interacting systems. This project will make progress on fundamental and long-standing questions concerning entanglement, chaos and transport in many-body quantum systems and quantum field theory, by building on connections between these fields that have recently emerged in studies of holographic quantum field theories and random quantum circuits. In particular: (i) We will develop effective field theory descriptions of many-body quantum chaos, which currently only exist for the special case of `maximally chaotic' systems. These theories would provide a universal framework for describing chaos across a wide range of systems. (ii) We will use connections between diffusion and chaos originally identified in holographic theories to develop fundamental bounds on transport in many-body quantum systems and quantum field theory. Such bounds would provide a general tool for understanding transport in strongly correlated materials, and could explain the existence of anomalous transport properties such as the linear resistivity found in strange metals. (iii) We will develop a coarse-grained description of entanglement dynamics in quantum field theory by generalising `entanglement membrane' techniques that arise in random quantum circuits, and apply these to gravitational systems to address the fate of quantum information during the black hole evaporation.