Skip to main content
SpringerLink
Log in

Fast scramblers, horizons and expander graphs

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We propose that local quantum systems defined on expander graphs provide a simple microscopic model for thermalization on quantum horizons. Such systems are automatically fast scramblers and are motivated from the membrane paradigm by a conformal transformation to the so-called optical metric.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  2. Y. Sekino and L. Susskind, Fast scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].

    Article  ADS  Google Scholar 

  3. L. Susskind, Addendum to fast scramblers, arXiv:1101.6048 [INSPIRE].

  4. T. Damour, Black hole Eddy currents, Phys. Rev. D 18 (1978) 3598 [INSPIRE].

    ADS  Google Scholar 

  5. K.S. Thorne, R.H. Price and D.A. Macdonald, Black holes: the membrane paradigm, Yale University Press, Yale, U.S.A. (1986) [INSPIRE].

    Google Scholar 

  6. L. Susskind and J. Lindesay, An introduction to black holes, information and the string theory revolution: the holographic universe, World Scientific, U.S.A. (2005) [INSPIRE].

    MATH  Google Scholar 

  7. J.L. Barbon and J.M. Magan, Chaotic fast scrambling at black holes, Phys. Rev. D 84 (2011) 106012 [arXiv:1105.2581] [INSPIRE].

    ADS  Google Scholar 

  8. J. Barbon and J. Magan, Fast scramblers of small size, JHEP 10 (2011) 035 [arXiv:1106.4786] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. L. Susskind, L. Thorlacius and J. Uglum, The stretched horizon and black hole complementarity, Phys. Rev. D 48 (1993) 3743 [hep-th/9306069] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  10. L. Susskind, The world as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. M. Edalati, W. Fischler, J.F. Pedraza and W. Tangarife Garcia, Fast scramblers and non-commutative gauge theories, JHEP 07 (2012) 043 [arXiv:1204.5748] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  12. S. Hoory, N. Linial and A. Widgerson, Expander graphs and their applications, Bull Amer. Math. Soc. 43 (2006) 439.

    Article  MathSciNet  MATH  Google Scholar 

  13. A. Lubotzky, Expander graphs in pure and applied mathematics, arXiv:1105.2389.

  14. N. Lashkari, D. Stanford, M. Hastings, T. Osborne and P. Hayden, Towards the fast scrambling conjecture, arXiv:1111.6580 [INSPIRE].

  15. A.O. Caldeira and A.J. Leggett, Path integral approach to quantum Brownian motion, Physica 121A (1983) 587.

    MathSciNet  ADS  Google Scholar 

  16. W.H. Zurek, Decoherence, einselection and the quantum origins of the classical, Rev. Mod. Phys. 75 (2003) 715 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. M. Schlosshauer, Decoherence and the quantum-to-classical transition, Springer, U.S.A. (2007).

    Google Scholar 

  18. R. Mosseri and J.F. Sadoc, The Bethe lattice: a regular tiling of the hyperbolic plane, J. Phys. Lett. Paris 43 (1982) 249.

    Article  Google Scholar 

  19. B. Söderberg, Bethe lattices in hyperbolic space Phys. Rev. E 47 (1993) 4582.

    ADS  Google Scholar 

  20. I. Sachs and S.N. Solodukhin, Horizon holography, Phys. Rev. D 64 (2001) 124023 [hep-th/0107173] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  21. C. Monthus and C. Texier, Random walk on the Bethe lattice and hyperbolic Brownian motion, J. Phys. A 29 (1996) 2399 [cond-mat/9509067].

    MathSciNet  ADS  Google Scholar 

  22. G. Gibbons and C. Warnick, Universal properties of the near-horizon optical geometry, Phys. Rev. D 79 (2009) 064031 [arXiv:0809.1571] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  23. G. ’t Hooft, On the quantum structure of a black hole, Nucl. Phys. B 256 (1985) 727 [INSPIRE].

    Article  ADS  Google Scholar 

  24. J. Barbón, Horizon divergences of fields and strings in black hole backgrounds, Phys. Rev. D 50 (1994)2712 [hep-th/9402004] [INSPIRE].

    ADS  Google Scholar 

  25. M.C. Gutzwiller, Chaos in classical and quantum mechanics, Springer, U.S.A. (1990).

    MATH  Google Scholar 

  26. N. Balazs and A. Voros, Chaos on the pseudosphere, Phys. Rept. 143 (1986) 109 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. D.N. Page, Average entropy of a subsystem, Phys. Rev. Lett. 71 (1993) 1291 [gr-qc/9305007] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. D.N. Page, Black hole information, hep-th/9305040 [INSPIRE].

  29. M. Hein et al., Entanglement in graph states and its applications, quant-ph/0602096.

  30. P. Candelas and J. Dowker, Field theories on conformally related space-times: some global considerations, Phys. Rev. D 19 (1979) 2902 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  31. H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. G. Festuccia and H. Liu, The arrow of time, black holes and quantum mixing of large-N Yang-Mills theories, JHEP 12 (2007) 027 [hep-th/0611098] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. N. Iizuka and J. Polchinski, A matrix model for black hole thermalization, JHEP 10 (2008) 028 [arXiv:0801.3657] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. N. Iizuka, T. Okuda and J. Polchinski, Matrix models for the black hole information paradox, JHEP 02 (2010) 073 [arXiv:0808.0530] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. C. Asplund, D. Berenstein and D. Trancanelli, Evidence for fast thermalization in the plane-wave matrix model, Phys. Rev. Lett. 107 (2011) 171602 [arXiv:1104.5469] [INSPIRE].

    Article  ADS  Google Scholar 

  36. J.M. Maldacena, Eternal black holes in Anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. L. Dyson, J. Lindesay and L. Susskind, Is there really a de Sitter/CFT duality?, JHEP 08 (2002)045 [hep-th/0202163] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. L. Dyson, M. Kleban and L. Susskind, Disturbing implications of a cosmological constant, JHEP 10 (2002) 011 [hep-th/0208013] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  39. N. Goheer, M. Kleban and L. Susskind, The trouble with de Sitter space, JHEP 07 (2003) 056 [hep-th/0212209] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. D. Birmingham, I. Sachs and S.N. Solodukhin, Relaxation in conformal field theory, Hawking-Page transition and quasinormal normal modes, Phys. Rev. D 67 (2003) 104026 [hep-th/0212308] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  41. J. Barbon and E. Rabinovici, Very long time scales and black hole thermal equilibrium, JHEP 11 (2003) 047 [hep-th/0308063] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. J. Barbon and E. Rabinovici, Long time scales and eternal black holes, Fortsch. Phys. 52 (2004)642 [hep-th/0403268] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  43. J. Barbon and E. Rabinovici, Topology change and unitarity in quantum black hole dynamics, hep-th/0503144 [INSPIRE].

  44. M. Kleban, M. Porrati and R. Rabadán, Poincaré recurrences and topological diversity, JHEP 10 (2004) 030 [hep-th/0407192] [INSPIRE].

    Article  ADS  Google Scholar 

  45. J. Abajo-Arrastia, J. Aparicio and E. Lopez, Holographic evolution of entanglement entropy, JHEP 11 (2010) 149 [arXiv:1006.4090] [INSPIRE].

    Article  ADS  Google Scholar 

  46. V. Balasubramanian et al., Thermalization of strongly coupled field theories, Phys. Rev. Lett. 106 (2011)191601 [arXiv:1012.4753] [INSPIRE].

    Article  ADS  Google Scholar 

  47. V. Balasubramanian et al., Holographic thermalization, Phys. Rev. D 84 (2011) 026010 [arXiv:1103.2683] [INSPIRE].

    ADS  Google Scholar 

  48. J. Aparicio and E. Lopez, Evolution of two-point functions from holography, JHEP 12 (2011) 082 [arXiv:1109.3571] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto de F´ısica Teórica IFT UAM/CSIC, Facultad de Ciencias C-XVI, C.U. Cantoblanco, E-28049, Madrid, Spain

    José L. F. Barbón & Javier M. Magán

Authors
  1. José L. F. Barbón
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Javier M. Magán
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to José L. F. Barbón.

Additional information

ArXiv ePrint: 1204.6435

Rights and permissions

Reprints and permissions

About this article

Cite this article

Barbón, J.L.F., Magán, J.M. Fast scramblers, horizons and expander graphs. J. High Energ. Phys. 2012, 16 (2012). https://doi.org/10.1007/JHEP08(2012)016

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP08(2012)016

Keywords

Search

Navigation