# Sašo Grozdanov: From hydrodynamics to quantum chaos

Date: 3. 3. 2020

Source: Mathematical physics seminar

Source: Mathematical physics seminar

Četrtek 5.3.2020, ob 11:15h, Kuščerjev seminar, Jadranska 19.

Hydrodynamics is a theory of the 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. For any
collective physical mode, hydrodynamics will predict a dispersion
relation that expresses this mode’s frequency in terms of an 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 (fractional powers of) 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 (AdS/CFT), the critical points
correspond to level-crossings in the quasinormal spectrum of a dual
black hole. Interestingly, holography implies that the convergence radii
can be orders of magnitude larger than what may be naively expected.
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 new and special property of
quantum 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).