We all carry an intuitive sense of chaos. The Cambridge Dictionary describes it as “a state of total confusion with no order.” In science, chaos refers to the loss of predictability in a physical system or mathematical model that arises from the sheer scale and complexity of its parts. More precisely, chaos is a non-equilibrium phenomenon in which the time evolution of a system is extraordinarily sensitive to its initial conditions: minuscule, often imperceptible, changes can dramatically alter its long-term behaviour – the butterfly effect.
That definition works well for classical systems. Quantum systems, by contrast, do not follow definite trajectories, which makes it harder to pin down what it means for them to be chaotic. A particularly promising way to quantify quantum chaos uses out-of-time-ordered correlators (OTOCs); see García-Mata et al. for a review. In a chaotic quantum system, an OTOC starts near zero, grows exponentially for a while, and then fluctuates around a saturation value once the system has lost all memory of its initial state. In non-chaotic systems, the period of growth is absent.
My research programme at Oxford with Márk Mezei builds low-energy effective field theories for chaotic quantum systems. These models let us compute OTOCs and explore how chaos interacts with other non-equilibrium phenomena, such as dissipation. We use modern Schwinger–Keldysh techniques, which evolve several copies of a system forwards and backwards in time, together with insights from holography. Our recent paper on the fluctuating hydrodynamics of the SYK lattice – a solvable model of a chaotic quantum system – appeared in April 2026.
Papers
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Out-of-time-order hydrodynamics and scrambling
In chaotic quantum systems, from black holes to strongly interacting materials, information about a small disturbance quickly spreads through the whole system, a process called scrambling. Detecting it requires evolving the system forwards and backwards in time twice, beyond the reach of ordinary hydrodynamics, our theory of how energy flows. We extend hydrodynamics to this setting using an extra symmetry acting on time, and derive it exactly from the SYK lattice, a solvable model of interacting quantum particles. There, energy flow scrambles information as fast as quantum mechanics allows.
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All-order fluctuating hydrodynamics of the SYK lattice
Hydrodynamics describes how energy and charge flow in almost any system at long distances and late times, but deriving it from the underlying microscopic physics is notoriously hard, especially when the particles interact strongly. We do this for the SYK lattice, a solvable model of strongly interacting quantum particles that has become a playground for quantum chaos. We show how hydrodynamics, random fluctuations included, emerges from the model at low energies, and pin down every ingredient of the theory, including the infinite series of corrections that are usually neglected.
Talks
Schwinger-Keldysh hydrodynamics of the SYK lattice
