Chaos and Scrambling in many-body quantum systems

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A long standing issue has been to understand chaos in quantum many body systems. In particular, whilst chaos has long been understood in classical dynamics and in single-particle quantum mechanics, it has remained extremely challenging to understand what is mean by chaos in a a many-body quantum system. Nevertheless, the question of quantum chaos is of central importance in understanding many-body quantum dynamics, not least due its connection to how quantum mechanical systems thermalise. Over the last several years, a new characterisation of chaos in many-body quantum systems has been provided through a characterisation of information scrambling, the decay of out of time ordered correlators, and efficient operator spreading. The aim of this project will be to study new signatures of chaos and scrambling in many-body quantum systems, using techniques from holographic quantum theories and and quantum information theory. In particular, over the last few years there have emerged surprising connections between scrambling in many-body quantum systems and hydrodynamics, including surprising connections between energy diffusion and chaos. Based on these connections, [1] proposed an effective hydrodynamic theory for scrambling in maximally chaotic systems, in which the scrambling of operators arises due to interactions with hydrodynamic degrees of freedom. One output of this theory was a prediction of a new phenomenon in maximally chaotic systems known as pole-skipping. This refers to a precise connection between the Lyapunov exponent and butterfly velocity that appear in out-of-time ordered correlation functions and the dispersion relations of hydrodynamic modes (collective excitations) of the system. An important tool for testing this phenomenon are holographic quantum field theories. Such field theories have a dual mathematical description in terms of the dynamics of black holes in anti-de Sitter space, using which one can compute both out-of-time ordered correlation functions and hydrodynamic modes of these quantum field theories.The initial aim of this project will be to study the pole-skipping phenomenon mentioned above, in the context of quantum systems which are holographically dual to the rotating Myers-Perry-AdS black hole. Future work is likely to explore other aspects of chaos in many-body quantum systems. For example, this could include studying entanglement dynamics in many-body quantum systems or studying scrambling in other toy models e.g. quantum circuits.