CoChat
Sign Up
Cited by 158

The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.

Many-body chaos and energy dynamics in holography

Blake, Mike, Davison, Richard A., Grozdanov, Sašo, Liu, Hong·2018·Journal of High Energy Physics
DOI 10.1007/jhep10(2018)035
Open this paper in CoChat — free account

Abstract

A bstract: Recent developments have indicated that in addition to out-of-time ordered correlation functions (OTOCs), quantum chaos also has a sharp manifestation in the thermal energy density two-point functions, at least for maximally chaotic systems. The manifestation, referred to as pole-skipping, concerns the analytic behaviour of energy density two-point functions around a special point ω = iλ , k = iλ/v B in the complex frequency and momentum plane. Here λ and v B are the Lyapunov exponent and butterfly velocity characterising quantum chaos. In this paper we provide an argument that the phenomenon of pole-skipping is universal for general finite temperature systems dual to Einstein gravity coupled to matter. In doing so we uncover a surprising universal feature of the linearised Einstein equations around a static black hole geometry. We also study analytically a holographic axion model where all of the features of our general argument as well as the pole-skipping phenomenon can be verified in detail.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1007/jhep10(2018)035

Cites

2 of 2 references verified0 citation errors · 0 not checkable

Statistics

Figures

Image 1
CC-BY · From the PDF
Figure 2 These plots show the dispersion relation ω ( k ) of the hydrodynamic pole in (3.7) as a function of imaginary k for the choices m/T = 1 / 100 and m/T = 100. The blue lines are the hydrodynamic approximations (3.36) (left panel) and (3.37) (right panel) to the small k hydrodynamic behaviour. The black dots correspond to the exact dispersion relation extracted from our numerics. Despite the qualitatively different small k behaviour, in all cases we find this dispersion relation passes through the special point (1.3) such that ω ( ik 0 ) = iλ for k 0 = λ/v B .
Figure 2 These plots show the dispersion relation ω ( k ) of the hydrodynamic pole in (3.7) as a function of imaginary k for the choices m/T = 1 / 100 and m/T = 100. The blue lines are the hydrodynamic approximations (3.36) (left panel) and (3.37) (right panel) to the small k hydrodynamic behaviour. The black dots correspond to the exact dispersion relation extracted from our numerics. Despite the qualitatively different small k behaviour, in all cases we find this dispersion relation passes through the special point (1.3) such that ω ( ik 0 ) = iλ for k 0 = λ/v B .CC-BY · From the PDF
Figure 3 (a) The red line plots the butterfly velocity v B = λ/k 0 as determined from the analytic formula (3.3). The black dots correspond to λ/k 1 where k 1 is extracted as the wavevector for which the numerical dispersion relation for the hydrodynamic pole satisfies ω ( ik 1 ) = iλ . If the pole passes through (1.3) then we should have λ/k 1 = v B which indeed holds for all m/T . (b) The red line plots the analytic formula (3.28) for the slope of the line of poles in the energy density correlator as it passes through the point (1.3). The dots correspond to the values of the slope extracted from the numerical calculations of the dispersion relation. Note that m/T →∞ corresponds to m = √ 6 r 0 , which is the upper limit shown on each plot.
Figure 3 (a) The red line plots the butterfly velocity v B = λ/k 0 as determined from the analytic formula (3.3). The black dots correspond to λ/k 1 where k 1 is extracted as the wavevector for which the numerical dispersion relation for the hydrodynamic pole satisfies ω ( ik 1 ) = iλ . If the pole passes through (1.3) then we should have λ/k 1 = v B which indeed holds for all m/T . (b) The red line plots the analytic formula (3.28) for the slope of the line of poles in the energy density correlator as it passes through the point (1.3). The dots correspond to the values of the slope extracted from the numerical calculations of the dispersion relation. Note that m/T →∞ corresponds to m = √ 6 r 0 , which is the upper limit shown on each plot.CC-BY · From the PDF

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 2 references

Research works printed but not linked: 46

  1. A.I. Larkin and Y.N. Ovchinnikov, Quasiclassical Method in the Theory of Superconductivity, Sov. Phys. JETP 28 (1969) 1200.
  2. S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE]. · DOI · Paper page
  3. D.A. Roberts, D. Stanford and L. Susskind, Localized shocks, JHEP 03 (2015) 051 [arXiv:1409.8180] [INSPIRE]. · DOI
  4. J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE]. · DOI
  5. A. Kitaev, Hidden correlations in the Hawking radiation and thermal noise, talk given at Fundamental Physics Prize Symposium, 10 November 2014.
  6. A. Kitaev and S.J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, JHEP 05 (2018) 183 [arXiv:1711.08467] [INSPIRE]. · DOI · Paper page
  7. J. Polchinski, Chaos in the black hole S-matrix, arXiv:1505.08108 [INSPIRE]. · arXiv
  8. J. Polchinski and V. Rosenhaus, The Spectrum in the Sachdev-Ye-Kitaev Model, JHEP 04 (2016) 001 [arXiv:1601.06768] [INSPIRE]. · DOI · Paper page
  9. J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE]. · DOI · Paper page
  10. J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE]. · DOI · Paper page
  11. Y. Gu, X.-L. Qi and D. Stanford, Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models, JHEP 05 (2017) 125 [arXiv:1609.07832] [INSPIRE]. · DOI
  12. R.A. Davison, W. Fu, A. Georges, Y. Gu, K. Jensen and S. Sachdev, Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography, Phys. Rev. B 95 (2017) 155131 [arXiv:1612.00849] [INSPIRE]. · DOI
  13. A.A. Patel and S. Sachdev, Quantum chaos on a critical Fermi surface, Proc. Nat. Acad. Sci. 114 (2017) 1844 [arXiv:1611.00003] [INSPIRE]. · DOI
  14. I.L. Aleiner, L. Faoro and L.B. Ioffe, Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves, Annals Phys. 375 (2016) 378 [arXiv:1609.01251] [INSPIRE]. · DOI
  15. A. Nahum, S. Vijay and J. Haah, Operator Spreading in Random Unitary Circuits, Phys. Rev. X 8 (2018) 021014 [arXiv:1705.08975] [INSPIRE]. · DOI
  16. V. Khemani, D.A. Huse and A. Nahum, Velocity-dependent Lyapunov exponents in many-body quantum, semi-classical and classical chaos, arXiv:1803.05902 [INSPIRE]. · arXiv
  17. I. Kukuljan, S. Grozdanov and T. Prosen, Weak Quantum Chaos, Phys. Rev. B 96 (2017) 060301 [arXiv:1701.09147] [INSPIRE]. · DOI
  18. E. Ott, Chaos in Dynamical Systems, 2 edition, Cambridge University Press (2002). · DOI
  19. P. Gaspard, Chaos, Scattering and Statistical Mechanics, Cambridge Nonlinear Science Series, Cambridge University Press (1998). · DOI
  20. M. Blake, Universal Charge Diffusion and the Butterfly Effect in Holographic Theories, Phys. Rev. Lett. 117 (2016) 091601 [arXiv:1603.08510] [INSPIRE]. · DOI
  21. M. Blake, Universal Diffusion in Incoherent Black Holes, Phys. Rev. D 94 (2016) 086014 [arXiv:1604.01754] [INSPIRE]. · DOI
  22. M. Blake and A. Donos, Diffusion and Chaos from near AdS 2 horizons, JHEP 02 (2017) 013 [arXiv:1611.09380] [INSPIRE]. · DOI
  23. M. Blake, R.A. Davison and S. Sachdev, Thermal diffusivity and chaos in metals without quasiparticles, Phys. Rev. D 96 (2017) 106008 [arXiv:1705.07896] [INSPIRE]. · DOI
  24. S. Grozdanov, K. Schalm and V. Scopelliti, Black hole scrambling from hydrodynamics, Phys. Rev. Lett. 120 (2018) 231601 [arXiv:1710.00921] [INSPIRE]. · DOI · Paper page
  25. M. Blake, H. Lee and H. Liu, A quantum hydrodynamical description for scrambling and many-body chaos, arXiv:1801.00010 [INSPIRE]. · arXiv
  26. S. Grozdanov, K. Schalm and V. Scopelliti, Kinetic theory for classical and quantum many-body chaos, arXiv:1804.09182 [INSPIRE]. · arXiv
  27. A. Lucas, Constraints on hydrodynamics from many-body quantum chaos, arXiv:1710.01005 [INSPIRE]. · arXiv
  28. T. Hartman, S.A. Hartnoll and R. Mahajan, Upper Bound on Diffusivity, Phys. Rev. Lett. 119 (2017) 141601 [arXiv:1706.00019] [INSPIRE]. · DOI
  29. R.A. Davison, S.A. Gentle and B. Goutéraux, Slow relaxation and diffusion in holographic quantum critical phases, arXiv:1808.05659 [INSPIRE]. · arXiv
  30. F.M. Haehl and M. Rozali, Effective Field Theory for Chaotic CFTs, arXiv:1808.02898 [INSPIRE]. · arXiv
  31. T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP 05 (2014) 101 [arXiv:1311.5157] [INSPIRE]. · DOI
  32. R.A. Davison and B. Goutéraux, Momentum dissipation and effective theories of coherent and incoherent transport, JHEP 01 (2015) 039 [arXiv:1411.1062] [INSPIRE]. · DOI
  33. D.A. Roberts and B. Swingle, Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories, Phys. Rev. Lett. 117 (2016) 091602 [arXiv:1603.09298] [INSPIRE]. · DOI
  34. D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE]. · DOI · Paper page
  35. P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [INSPIRE]. · DOI
  36. C.P. Herzog, The Hydrodynamics of M-theory, JHEP 12 (2002) 026 [hep-th/0210126] [INSPIRE]. · DOI
  37. S. Grozdanov and N. Kaplis, Constructing higher-order hydrodynamics: The third order, Phys. Rev. D 93 (2016) 066012 [arXiv:1507.02461] [INSPIRE]. · DOI
  38. R.A. Davison and A. Parnachev, Hydrodynamics of cold holographic matter, JHEP 06 (2013) 100 [arXiv:1303.6334] [INSPIRE]. · DOI
  39. G. Compère, The Kerr/CFT correspondence and its extensions, Living Rev. Rel. 15 (2012) 11 [arXiv:1203.3561] [INSPIRE]. · DOI
  40. S. Grozdanov and A.O. Starinets, Second-order transport, quasinormal modes and zero-viscosity limit in the Gauss-Bonnet holographic fluid, JHEP 03 (2017) 166 [arXiv:1611.07053] [INSPIRE]. · DOI
  41. P. Bueno, P.A. Cano and A. Ruipérez, Holographic studies of Einsteinian cubic gravity, JHEP 03 (2018) 150 [arXiv:1802.00018] [INSPIRE]. · DOI
  42. A. Donos, J.P. Gauntlett and V. Ziogas, Diffusion for Holographic Lattices, JHEP 03 (2018) 056 [arXiv:1710.04221] [INSPIRE]. · DOI
  43. M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, Viscosity Bound Violation in Higher Derivative Gravity, Phys. Rev. D 77 (2008) 126006 [arXiv:0712.0805] [INSPIRE]. · DOI
  44. S. Grozdanov, N. Kaplis and A.O. Starinets, From strong to weak coupling in holographic models of thermalization, JHEP 07 (2016) 151 [arXiv:1605.02173] [INSPIRE]. · DOI
  45. D. Vegh, Holography without translational symmetry, arXiv:1301.0537 [INSPIRE]. · arXiv
  46. M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119] [INSPIRE]. · DOI

Cited by

Sorted by citations

Metadata

Authors
Blake, M., Davison, R. A., Grozdanov, S., & Liu, H.
Venue
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Published
2018-10
Volume
2018
Issue
10
ISSN
1029-8479
DOI
10.1007/jhep10(2018)035
Cited by
158
References
2
Language
en
Licence

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review