A quantum hydrodynamical description for scrambling and many-body chaos
By Mike Blake, Hyunseok Lee, Hong Liu. Journal of High Energy Physics, 2017
173 citations recorded by the source corpus.
A bstractRecent studies of out-of-time ordered thermal correlation functions (OTOC) in holographic systems and in solvable models such as the Sachdev-Ye-Kitaev (SYK) model have yielded new insights into manifestations of many-body chaos. So far the chaotic behavior has been obtained through explicit calculations in specific models. In this paper we propose a unified description of the exponential growth and ballistic butterfly spreading of OTOCs across different systems using a newly formulated “quantum hydrodynamics,” which is valid at finite ℏ and to all orders in derivatives. The scrambling of a generic few-body operator in a chaotic system is described as building up a “hydrodynamic cloud,” and the exponential growth of the cloud arises from a shift symmetry of the hydrodynamic action. The shift symmetry also shields correlation functions of the energy density and flux, and time ordered correlation functions of generic operators from exponential growth, while leads to chaotic behavior in OTOCs. The theory also predicts an interesting phenomenon of the skipping of a pole at special values of complex frequency and momentum in two-point functions of energy density and flux. This pole-skipping phenomenon may be considered as a “smoking gun” for the hydrodynamic origin of the chaotic mode. We also discuss the possibility that such a hydrodynamic description could be a hallmark of maximally chaotic systems.
Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/e0e6b5307d92ca24fae7d7c7cff168ca782677fa
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Citations in the corpus
- Many-body chaos and energy dynamics in holography (2018, background): “As emphasised in [27], the phenomenon of pole-skipping can be considered as a “smokinggun” for the fact quantum many-body chaos is tied with energy conservation.”
- The complex life of hydrodynamic modes (2019, background): “In the sound channel of the energy-momentum tensor retarded two-point function, the pole-skipping has been studied in the context of holography [29, 31, 32], effective field theory [30] and twodimensional conformal field theory in the limit of large central charge [70].”