A quantum hydrodynamical description for scrambling and many-body chaos

Blake, Mike; Lee, Hyunseok; Liu, Hong

doi:10.1007/JHEP10(2018)127

A quantum hydrodynamical description for scrambling and many-body chaos

Journal Article · Fri Oct 19 00:00:00 EDT 2018 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP10(2018)127· OSTI ID:1483400

Blake, Mike ^[1]; Lee, Hyunseok ^[2]; Liu, Hong ^[2]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Recent 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. Here, we also discuss the possibility that such a hydrodynamic description could be a hallmark of maximally chaotic systems.

View Accepted Manuscript (DOE)

Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

Grant/Contract Number:: SC0012567

OSTI ID:: 1483400

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 10 Vol. 2018; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Quantum information scrambling after a quantum quench Alba, Vincenzo; Calabrese, Pasquale arXiv https://doi.org/10.48550/arxiv.1903.09176	text	January 2019

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