2018/01/31 by Mike Blake, Hyunseok Lee, Hong Liu · 183 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Chaotic #Classical mechanics #Cosmology and Gravitation Theories #Mathematics #Momentum (technical analysis) #Operator (biology) #Physics #Quantum #Quantum chaos #Quantum dynamics #Quantum many-body systems #Quantum mechanics #Scrambling #Statistical physics #cond-mat.str-el #hep-th #nlin.CD #nucl-th #quant-ph
paper · pdf · doi:10.1007/jhep10(2018)127
published in Journal of High Energy Physics 2018(10) (Springer Nature) · 48 pages, 9 figures. v2: references added, various clarifications made including an expanded discussion of predictions in the introduction and an expanded discussion of four-point functions, v3: journal version
openalex publication_date 2018/10/01 · arxiv created 2018/10/15 · arxiv updated 2018/11/14 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
A bstract 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. We also discuss the possibility that such a hydrodynamic description could be a hallmark of maximally chaotic systems.