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Scrambling, chaos, and operator complexity

Thomas Scaffidi (U Toronto)
Monday, January 3, 2022 - 4:00pm to 5:00pm

Chaos theory studies the extreme sensitivity to initial conditions which occurs in complex physical systems. This "butterfly effect" is far from a theoretical curiosity since it provides a microscopic mechanism for the emergence of hydrodynamics at macroscopic scales. Extending the notion of classical chaos to the quantum realm has been an ongoing area of research for decades. Recently, progress in the study of quantum information and holography has led to a new putative definition of quantum chaos, known as scrambling, which measures the ever growing complexity of simple operators under time evolution. Although scrambling is a useful concept for non-local large-N theories like the Sachdev-Ye-Kitaev model, it has severe limitations when discussing more general systems. In this colloquium, I will show how to overcome these limitations by introducing a new measure of operator complexity called Krylov complexity which is broadly applicable to strongly correlated quantum systems, and which happens to be related to observables routinely measured in NMR experiments. Finally, I will argue that scrambling should be distinguished from chaos due to fundamental differences between them at the semiclassical level.

Video recording (UW only)

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