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Résumé |
Bounds on transport represent a way of understanding allowable regimes of quantum
and classical dynamics. Numerous such bounds have been proposed, either for
classes of theories or (by using general heuristic arguments) universally for all
theories. Few are exact and inviolable. In this talk, I will present new methods
for deriving exact, rigorous, and sharp bounds on all coefficients of hydrodynamic
dispersion relations, including diffusivity and the speed of sound. These general
techniques combine analytic properties of hydrodynamics and the theory of
univalent (complex holomorphic and injective) functions. Concrete examples will
include bounds that relate transport to quantum chaos through 'pole-skipping' as
well as bounds without relation to chaos, such as the conformal bound on the speed
of sound. I will also outline a set of general observations regarding the
univalence properties of diffusion and sound in holographic models. Finally, I
will discuss how these ideas could be generally applicable to constraining any
effective field theory, not only hydrodynamics. |
