Black Hole Scrambling from Hydrodynamics
Abstract
We argue that the gravitational shock wave computation used to extract the scrambling rate in strongly coupled quantum theories with a holographic dual is directly related to probing the system’s hydrodynamic sound modes. The information recovered from the shock wave can be reconstructed in terms of purely diffusionlike, linearized gravitational waves at the horizon of a single-sided black hole with specific regularity-enforced imaginary values of frequency and momentum. In two-derivative bulk theories, this horizon “diffusion” can be related to late-time momentum diffusion via a simple relation, which ceases to hold in higher-derivative theories. We then show that the same values of imaginary frequency and momentum follow from a dispersion relation of a hydrodynamic sound mode. The frequency, momentum, and group velocity give the holographic Lyapunov exponent and the butterfly velocity. Moreover, at this special point along the sound dispersion relation curve, the residue of the retarded longitudinal stress-energy tensor two-point function vanishes. This establishes a direct link between a hydrodynamic sound mode at an analytically continued, imaginary momentum and the holographic butterfly effect. Furthermore, our results imply that infinitely strongly coupled, large- Nc holographic theories exhibit properties similar to classical dilute gases; there, late-time equilibration and early-time scrambling are alsomore »
- Authors:
- Publication Date:
- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1441030
- Alternate Identifier(s):
- OSTI ID: 1498974
- Grant/Contract Number:
- SC0011090
- Resource Type:
- Published Article
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Name: Physical Review Letters Journal Volume: 120 Journal Issue: 23; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Grozdanov, Sašo, Schalm, Koenraad, and Scopelliti, Vincenzo. Black Hole Scrambling from Hydrodynamics. United States: N. p., 2018.
Web. doi:10.1103/PhysRevLett.120.231601.
Grozdanov, Sašo, Schalm, Koenraad, & Scopelliti, Vincenzo. Black Hole Scrambling from Hydrodynamics. United States. https://doi.org/10.1103/PhysRevLett.120.231601
Grozdanov, Sašo, Schalm, Koenraad, and Scopelliti, Vincenzo. Thu .
"Black Hole Scrambling from Hydrodynamics". United States. https://doi.org/10.1103/PhysRevLett.120.231601.
@article{osti_1441030,
title = {Black Hole Scrambling from Hydrodynamics},
author = {Grozdanov, Sašo and Schalm, Koenraad and Scopelliti, Vincenzo},
abstractNote = {We argue that the gravitational shock wave computation used to extract the scrambling rate in strongly coupled quantum theories with a holographic dual is directly related to probing the system’s hydrodynamic sound modes. The information recovered from the shock wave can be reconstructed in terms of purely diffusionlike, linearized gravitational waves at the horizon of a single-sided black hole with specific regularity-enforced imaginary values of frequency and momentum. In two-derivative bulk theories, this horizon “diffusion” can be related to late-time momentum diffusion via a simple relation, which ceases to hold in higher-derivative theories. We then show that the same values of imaginary frequency and momentum follow from a dispersion relation of a hydrodynamic sound mode. The frequency, momentum, and group velocity give the holographic Lyapunov exponent and the butterfly velocity. Moreover, at this special point along the sound dispersion relation curve, the residue of the retarded longitudinal stress-energy tensor two-point function vanishes. This establishes a direct link between a hydrodynamic sound mode at an analytically continued, imaginary momentum and the holographic butterfly effect. Furthermore, our results imply that infinitely strongly coupled, large- Nc holographic theories exhibit properties similar to classical dilute gases; there, late-time equilibration and early-time scrambling are also controlled by the same dynamics.},
doi = {10.1103/PhysRevLett.120.231601},
journal = {Physical Review Letters},
number = 23,
volume = 120,
place = {United States},
year = {Thu Jun 07 00:00:00 EDT 2018},
month = {Thu Jun 07 00:00:00 EDT 2018}
}
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Cited by: 86 works
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Figures / Tables:
FIG. 1. : Dispersion relations of the hydrodynamic sound modes, plotted for imaginary dimensionless w≡ $ω$=2$πT$ and q≡ $k$=2$πT$. The blue lines depict the third-order hydrodynamic result [55] and the red crosses the numerically computed more » $^*_±$ (q). Dashed lines indicate the values of $ω$ = $iλ$$L$ and $k$ = $iμ$. The dotted line is the linear dispersion relation w = $v$$B$q. The inlay depicts an enlarged plot around $k$ = $iμ$.
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Works referenced in this record:
Coupling constant dependence in the thermodynamics of N = 4 supersymmetric Yang-Mills theory
journal, November 1998
- Gubser, Steven S.; Klebanov, Igor R.; Tseytlin, Arkady A.
- Nuclear Physics B, Vol. 534, Issue 1-2
Diffusion and chaos from near AdS2 horizons
journal, February 2017
- Blake, Mike; Donos, Aristomenis
- Journal of High Energy Physics, Vol. 2017, Issue 2
Finite coupling corrections to holographic predictions for hot QCD
journal, November 2015
- Waeber, Sebastian; Schäfer, Andreas; Vuorinen, Aleksi
- Journal of High Energy Physics, Vol. 2015, Issue 11
Black holes as mirrors: quantum information in random subsystems
journal, September 2007
- Hayden, Patrick; Preskill, John
- Journal of High Energy Physics, Vol. 2007, Issue 09
Kinetic Models and the Linearized Boltzmann Equation
journal, January 1959
- Gross, Eugene P.; Jackson, E. Atlee
- Physics of Fluids, Vol. 2, Issue 4
Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
journal, March 2005
- Kovtun, P. K.; Son, D. T.; Starinets, A. O.
- Physical Review Letters, Vol. 94, Issue 11
From AdS/CFT correspondence to hydrodynamics
journal, September 2002
- Policastro, Giuseppe; Son, Dam T.; Starinets, Andrei O.
- Journal of High Energy Physics, Vol. 2002, Issue 09
Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
journal, September 2002
- Son, Dam T.; Starinets, Andrei O.
- Journal of High Energy Physics, Vol. 2002, Issue 09
Holographic thermalization in $${{\mathcal N}}=4$$ N = 4 super Yang–Mills theory at finite coupling
journal, February 2014
- Stricker, Stefan A.
- The European Physical Journal C, Vol. 74, Issue 2
Holographic constraints on Bjorken hydrodynamics at finite coupling
journal, October 2017
- DiNunno, Brandon S.; Grozdanov, Sašo; Pedraza, Juan F.
- Journal of High Energy Physics, Vol. 2017, Issue 10
On gravitational shock waves in curved spacetimes
journal, February 1995
- Sfetsos, Konstadinos
- Nuclear Physics B, Vol. 436, Issue 3
From AdS/CFT correspondence to hydrodynamics. II. Sound waves
journal, December 2002
- Policastro, Giuseppe; Son, Dam T.; Starinets, Andrei O.
- Journal of High Energy Physics, Vol. 2002, Issue 12
Shear Viscosity of Strongly Coupled Supersymmetric Yang-Mills Plasma
journal, August 2001
- Policastro, G.; Son, D. T.; Starinets, A. O.
- Physical Review Letters, Vol. 87, Issue 8
Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography
journal, April 2017
- Davison, Richard A.; Fu, Wenbo; Georges, Antoine
- Physical Review B, Vol. 95, Issue 15
On the rate of mixing of Axiom A flows
journal, October 1985
- Pollicott, Mark
- Inventiones Mathematicae, Vol. 81, Issue 3
Black holes and the butterfly effect
journal, March 2014
- Shenker, Stephen H.; Stanford, Douglas
- Journal of High Energy Physics, Vol. 2014, Issue 3
Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
journal, May 2017
- Gu, Yingfei; Qi, Xiao-Liang; Stanford, Douglas
- Journal of High Energy Physics, Vol. 2017, Issue 5
Fast scramblers
journal, October 2008
- Sekino, Yasuhiro; Susskind, L.
- Journal of High Energy Physics, Vol. 2008, Issue 10
Universal diffusion in incoherent black holes
journal, October 2016
- Blake, Mike
- Physical Review D, Vol. 94, Issue 8
Coupling Constant Corrections in a Holographic Model of Heavy Ion Collisions
journal, July 2017
- Grozdanov, Sašo; van der Schee, Wilke
- Physical Review Letters, Vol. 119, Issue 1
Upper Bound on Diffusivity
journal, October 2017
- Hartman, Thomas; Hartnoll, Sean A.; Mahajan, Raghu
- Physical Review Letters, Vol. 119, Issue 14
Divergence of classical trajectories and weak localization
journal, November 1996
- Aleiner, I. L.; Larkin, A. I.
- Physical Review B, Vol. 54, Issue 20
Lectures on hydrodynamic fluctuations in relativistic theories
journal, November 2012
- Kovtun, Pavel
- Journal of Physics A: Mathematical and Theoretical, Vol. 45, Issue 47
Holography and Colliding Gravitational Shock Waves in Asymptotically Spacetime
journal, January 2011
- Chesler, Paul M.; Yaffe, Laurence G.
- Physical Review Letters, Vol. 106, Issue 2
Incoherent thermal transport from dirty black holes
journal, March 2016
- Grozdanov, Sašo; Lucas, Andrew; Schalm, Koenraad
- Physical Review D, Vol. 93, Issue 6
Holographic butterfly effect at quantum critical points
journal, October 2017
- Ling, Yi; Liu, Peng; Wu, Jian-Pin
- Journal of High Energy Physics, Vol. 2017, Issue 10
Onset of many-body chaos in the model
journal, September 2017
- Chowdhury, Debanjan; Swingle, Brian
- Physical Review D, Vol. 96, Issue 6
Quasinormal modes and holography
journal, October 2005
- Kovtun, Pavel K.; Starinets, Andrei O.
- Physical Review D, Vol. 72, Issue 8
Equilibration and hydrodynamics at strong and weak coupling
journal, November 2017
- van der Schee, Wilke
- Nuclear Physics A, Vol. 967
Lower bounds on high-temperature diffusion constants from quadratically extensive almost-conserved operators
journal, January 2014
- Prosen, Tomaž
- Physical Review E, Vol. 89, Issue 1
Role of divergence of classical trajectories in quantum chaos
journal, February 1997
- Aleiner, I. L.; Larkin, A. I.
- Physical Review E, Vol. 55, Issue 2
Quantum chaos on a critical Fermi surface
journal, February 2017
- Patel, Aavishkar A.; Sachdev, Subir
- Proceedings of the National Academy of Sciences, Vol. 114, Issue 8
Universal Charge Diffusion and the Butterfly Effect in Holographic Theories
journal, August 2016
- Blake, Mike
- Physical Review Letters, Vol. 117, Issue 9
Quantum Butterfly Effect in Weakly Interacting Diffusive Metals
journal, September 2017
- Patel, Aavishkar A.; Chowdhury, Debanjan; Sachdev, Subir
- Physical Review X, Vol. 7, Issue 3
Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories
journal, August 2016
- Roberts, Daniel A.; Swingle, Brian
- Physical Review Letters, Vol. 117, Issue 9
Schwinger-Keldysh propagators from AdS/CFT correspondence
journal, March 2003
- Herzog, Christopher P.; Son, Dam Thanh
- Journal of High Energy Physics, Vol. 2003, Issue 03
Weak quantum chaos
journal, August 2017
- Kukuljan, Ivan; Grozdanov, Sašo; Prosen, Tomaž
- Physical Review B, Vol. 96, Issue 6
A bound on chaos
journal, August 2016
- Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas
- Journal of High Energy Physics, Vol. 2016, Issue 8
Second-order transport, quasinormal modes and zero-viscosity limit in the Gauss-Bonnet holographic fluid
journal, March 2017
- Grozdanov, Sašo; Starinets, Andrei O.
- Journal of High Energy Physics, Vol. 2017, Issue 3
Largest Lyapunov Exponent for Many Particle Systems at Low Densities
journal, March 1998
- van Zon, R.; van Beijeren, H.; Dellago, Ch.
- Physical Review Letters, Vol. 80, Issue 10
Retarded correlators in kinetic theory: branch cuts, poles and hydrodynamic onset transitions
journal, June 2016
- Romatschke, Paul
- The European Physical Journal C, Vol. 76, Issue 6
Holography and hydrodynamics: diffusion on stretched horizons
journal, October 2003
- Kovtun, Pavel; Son, Dam T.; Starinets, Andrei O.
- Journal of High Energy Physics, Vol. 2003, Issue 10
Thermal diffusivity and chaos in metals without quasiparticles
journal, November 2017
- Blake, Mike; Davison, Richard A.; Sachdev, Subir
- Physical Review D, Vol. 96, Issue 10
Theory of universal incoherent metallic transport
journal, December 2014
- Hartnoll, Sean A.
- Nature Physics, Vol. 11, Issue 1
Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory
journal, January 2009
- Kats, Yevgeny; Petrov, Pavel
- Journal of High Energy Physics, Vol. 2009, Issue 01
Notes on hyperscaling violating Lifshitz and shear diffusion
journal, July 2017
- Kolekar, Kedar S.; Mukherjee, Debangshu; Narayan, K.
- Physical Review D, Vol. 96, Issue 2
Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains
journal, January 2017
- Gu, Yingfei; Lucas, Andrew; Qi, Xiao-Liang
- SciPost Physics, Vol. 2, Issue 3
Microscopic model of quantum butterfly effect: Out-of-time-order correlators and traveling combustion waves
journal, December 2016
- Aleiner, Igor L.; Faoro, Lara; Ioffe, Lev B.
- Annals of Physics, Vol. 375
Viscosity bound violation in higher derivative gravity
journal, June 2008
- Brigante, Mauro; Liu, Hong; Myers, Robert C.
- Physical Review D, Vol. 77, Issue 12
Localized shocks
journal, March 2015
- Roberts, Daniel A.; Stanford, Douglas; Susskind, Leonard
- Journal of High Energy Physics, Vol. 2015, Issue 3
Asymptotic Theory of the Boltzmann Equation
journal, January 1963
- Grad, Harold
- Physics of Fluids, Vol. 6, Issue 2
On the universal identity in second order hydrodynamics
journal, March 2015
- Grozdanov, S.; Starinets, A. O.
- Journal of High Energy Physics, Vol. 2015, Issue 3
Absence of Disorder-Driven Metal-Insulator Transitions in Simple Holographic Models
journal, November 2015
- Grozdanov, Sašo; Lucas, Andrew; Sachdev, Subir
- Physical Review Letters, Vol. 115, Issue 22
Resonances of chaotic dynamical systems
journal, February 1986
- Ruelle, David
- Physical Review Letters, Vol. 56, Issue 5
From strong to weak coupling in holographic models of thermalization
journal, July 2016
- Grozdanov, Sašo; Kaplis, Nikolaos; Starinets, Andrei O.
- Journal of High Energy Physics, Vol. 2016, Issue 7
Constructing higher-order hydrodynamics: The third order
journal, March 2016
- Grozdanov, Sašo; Kaplis, Nikolaos
- Physical Review D, Vol. 93, Issue 6
Works referencing / citing this record:
Stringy effects and the role of the singularity in holographic complexity
journal, September 2019
- Nally, Richard
- Journal of High Energy Physics, Vol. 2019, Issue 9
Effective field theory for chaotic CFTs
journal, October 2018
- Haehl, Felix M.; Rozali, Moshe
- Journal of High Energy Physics, Vol. 2018, Issue 10
A quantum hydrodynamical description for scrambling and many-body chaos
journal, October 2018
- Blake, Mike; Lee, Hyunseok; Liu, Hong
- Journal of High Energy Physics, Vol. 2018, Issue 10
The complex life of hydrodynamic modes
journal, November 2019
- Grozdanov, Sašo; Kovtun, Pavel K.; Starinets, Andrei O.
- Journal of High Energy Physics, Vol. 2019, Issue 11
Nonuniqueness of Green’s functions at special points
journal, December 2019
- Natsuume, Makoto; Okamura, Takashi
- Journal of High Energy Physics, Vol. 2019, Issue 12
Reentrant superconductivity in a quantum dot coupled to a Sachdev-Ye-Kitaev metal
journal, December 2019
- Cheipesh, Y.; Pavlov, A. I.; Scopelliti, V.
- Physical Review B, Vol. 100, Issue 22
Pole skipping with finite-coupling corrections
journal, December 2019
- Natsuume, Makoto; Okamura, Takashi
- Physical Review D, Vol. 100, Issue 12
Mutual Correlation in the Shock Wave Geometry
journal, August 2018
- Zeng, Xiao-Xiong; Shao, Hong-Bo; Li, Ling
- Advances in High Energy Physics, Vol. 2018
Recent Developments in the Holographic Description of Quantum Chaos
journal, March 2019
- Jahnke, Viktor
- Advances in High Energy Physics, Vol. 2019
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