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Title:
From the convergence of all-order hydrodynamics to microscopic quantum chaos
Speaker:
Abstract:
Hydrodynamics is a theory of collective properties of fluids and gases that can also be successfully applied to the description of the dynamics of quark-gluon plasma. It is an effective field theory formulated in terms of an infinite-order gradient expansion. Hydrodynamics predicts the dispersion relations of collective physical modes, which express the modes’ frequencies in terms of infinite series in powers of momentum. By using the theory of complex spectral curves from the mathematical field of algebraic geometry, I will describe how these dispersion relations can be understood as Puiseux series in complex momentum. The series have finite radii of convergence determined by the critical points of the associated spectral curves. For theories that admit a dual gravitational description through holography, the critical points correspond to level-crossings in the quasinormal spectrum of the dual black hole. Interestingly, holography implies that the convergence radii can be orders of magnitude larger than the naive expectation. This fact could help explain the ``unreasonable effectiveness of hydrodynamics” in describing the evolution of quark-gluon plasma. In the second part of my talk, I will discuss a recently discovered phenomenon called ``pole-skipping” that relates hydrodynamics to the underlying microscopic quantum many-body chaos. This special property of correlation functions allows for a precise analytic connection between resummed, all-order hydrodynamics and the properties of quantum chaos (the Lyapunov exponent and the butterfly velocity).
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