Quantum Chaos and Volumetric Spatiotemporal Correlations

Abstract: Chaotic systems are highly sensitive to a small perturbation, and are ubiquitous throughout biological sciences, physical sciences and even social sciences. Taking this as the underlying principle, we construct an operational notion for quantum chaos. Namely, we demand that the future state of a many-body, isolated quantum system is sensitive to past multitime operations on a small subpart of that system. By 'sensitive', we mean that the resultant states from two different perturbations cannot easily be transformed into each other. That is, the pertinent quantity is the complexity of the effect of the perturbation within the final state. From this intuitive metric, which we call the Butterfly Flutter Fidelity, we use the language of multitime quantum processes to identify a series of operational conditions on chaos, particularly the scaling of the spatiotemporal entanglement. Our criteria already contain routine notions and well-known diagnostics for quantum chaos. We then extend the criteria to include projected process ensembles, motivated by studies on deep thermalisation. Our results account for previous attempts to make sense of quantum chaos, such as the Peres-Loschmidt Echo, Dynamical Entropy, Tripartite Mutual Information, and Local-Operator Entanglement. Finally, we will present numerical results using the XXZ model and discuss how chaos leads to equilibration, Markovianisation, and thermalisation.

Reference: N Dowling, K Modi, PRX Quantum 5, 010314 (2024)

Bio: Kavan is a Professor at the Singapore University of Technology of Design. He got his PhD in 2008 from the University of Texas at Austin. He was a Research Fellow at the Centre for Quantum Technologies at the National University of Singapore, and then at Clarendon Labs at the University of Oxford. He was a Professor at Monash University and the Director of the Centre for Quantum Technologies at Transport for New South Wales (aka Quantum for New South Wales).