Advertisement

Holographic non-equilibrium heating

  • D. S. Ageev
  • I. Ya. Aref’eva
Open Access
Regular Article - Theoretical Physics
  • 65 Downloads

Abstract

We study the holographic entanglement entropy evolution after a global sharp quench of thermal state. After the quench, the system comes to equilibrium and the temperature increases from Ti to Tf . Holographic dual of this process is provided by an injection of a thin shell of matter in the black hole background. The quantitative characteristics of the evolution depend substantially on the size of the initial black hole. We show that characteristic regimes during non-equilibrium heating do not depend on the initial temperature and are the same as in thermalization. Namely these regimes are pre-local-equilibration quadratic growth, linear growth and saturation regimes of the time evolution of the holographic entanglement entropy. We study the initial temperature dependence of quantitative characteristics of these regimes and find that the critical exponents do not depend on the temperature, meanwhile the prefactors are the functions on the temperature.

Keywords

AdS-CFT Correspondence Holography and condensed matter physics (AdS/CMT) 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
  2. [2]
    S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  3. [3]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    U.H. Danielsson, E. Keski-Vakkuri and M. Kruczenski, Black hole formation in AdS and thermalization on the boundary, JHEP 02 (2000) 039 [hep-th/9912209] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions, in the book Gauge/String Duality, Hot QCD and Heavy Ion Collisions , Cambridge University Press, Cambridge U.K. (2014) [arXiv:1101.0618] [INSPIRE].
  8. [8]
    I. Ya. Aref’eva, Holographic approach to quark-gluon plasma in heavy ion collisions, Phys. Usp. 57 (2014) 527.Google Scholar
  9. [9]
    O. DeWolfe, S.S. Gubser, C. Rosen and D. Teaney, Heavy ions and string theory, Prog. Part. Nucl. Phys. 75 (2014) 86 [arXiv:1304.7794] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [INSPIRE].
  11. [11]
    R. Easther, R. Flauger, P. McFadden and K. Skenderis, Constraining holographic inflation with WMAP, JCAP 09 (2011) 030 [arXiv:1104.2040] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    J. Abajo-Arrastia, J. Aparicio and E. Lopez, Holographic Evolution of Entanglement Entropy, JHEP 11 (2010) 149 [arXiv:1006.4090] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  13. [13]
    V. Balasubramanian, A. Bernamonti, J. de Boer, N. Copland, B. Craps, E. Keski-Vakkuri et al., Holographic Thermalization, Phys. Rev. D 84 (2011) 026010 [arXiv:1103.2683] [INSPIRE].
  14. [14]
    J. Aparicio and E. Lopez, Evolution of Two-Point Functions from Holography, JHEP 12 (2011) 082 [arXiv:1109.3571] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    I. Ya. Aref’eva and I.V. Volovich, Holographic thermalization, Theor. Math. Phys. 174 (2013) 186 [Teor. Mat. Fiz. 174 (2013) 216] [arXiv:1211.6041].
  16. [16]
    I. Ya. Aref’eva, A. Bagrov and A.S. Koshelev, Holographic Thermalization from Kerr-AdS, JHEP 07 (2013) 170 [arXiv:1305.3267] [INSPIRE].
  17. [17]
    Y.-Z. Li, S.-F. Wu, Y.-Q. Wang and G.-H. Yang, Linear growth of entanglement entropy in holographic thermalization captured by horizon interiors and mutual information, JHEP 09 (2013) 057 [arXiv:1306.0210] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    T. Hartman and J. Maldacena, Time Evolution of Entanglement Entropy from Black Hole Interiors, JHEP 05 (2013) 014 [arXiv:1303.1080] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    H. Liu and S.J. Suh, Entanglement Tsunami: Universal Scaling in Holographic Thermalization, Phys. Rev. Lett. 112 (2014) 011601 [arXiv:1305.7244] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    H. Liu and S.J. Suh, Entanglement growth during thermalization in holographic systems, Phys. Rev. D 89 (2014) 066012 [arXiv:1311.1200] [INSPIRE].
  21. [21]
    S. Leichenauer and M. Moosa, Entanglement Tsunami in (1+1)-Dimensions, Phys. Rev. D 92 (2015) 126004 [arXiv:1505.04225] [INSPIRE].ADSMathSciNetGoogle Scholar
  22. [22]
    S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    D.S. Ageev and I. Ya. Aref’eva, Waking and scrambling in holographic heating up, Teor. Mat. Fiz. 193 (2017) 146 [arXiv:1701.07280] [INSPIRE].
  24. [24]
    V.E. Hubeny and H. Maxfield, Holographic probes of collapsing black holes, JHEP 03 (2014) 097 [arXiv:1312.6887] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    T. Albash and C.V. Johnson, Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches, New J. Phys. 13 (2011) 045017 [arXiv:1008.3027] [INSPIRE].
  26. [26]
    V. Balasubramanian, A. Bernamonti, J. de Boer, N. Copland, B. Craps, E. Keski-Vakkuri et al., Thermalization of Strongly Coupled Field Theories, Phys. Rev. Lett. 106 (2011) 191601 [arXiv:1012.4753] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    J. Aparicio and E. Lopez, Evolution of Two-Point Functions from Holography, JHEP 12 (2011) 082 [arXiv:1109.3571] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    D. Allahbakhshi, M. Alishahiha and A. Naseh, Entanglement Thermodynamics, JHEP 08 (2013) 102 [arXiv:1305.2728] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  31. [31]
    J. Bhattacharya, M. Nozaki, T. Takayanagi and T. Ugajin, Thermodynamical Property of Entanglement Entropy for Excited States, Phys. Rev. Lett. 110 (2013) 09160 [arXiv:1212.1164] [INSPIRE].Google Scholar
  32. [32]
    M. Nozaki, T. Numasawa, A. Prudenziati and T. Takayanagi, Dynamics of Entanglement Entropy from Einstein Equation, Phys. Rev. D 88 (2013) 026012 [arXiv:1304.7100] [INSPIRE].
  33. [33]
    D.D. Blanco, H. Casini, L.-Y. Hung and R.C. Myers, Relative Entropy and Holography, JHEP 08 (2013) 060 [arXiv:1305.3182] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    G. Wong, I. Klich, L.A. Pando Zayas and D. Vaman, Entanglement Temperature and Entanglement Entropy of Excited States, JHEP 12 (2013) 020 [arXiv:1305.3291] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    U.H. Danielsson, E. Keski-Vakkuri and M. Kruczenski, Spherically collapsing matter in AdS, holography and shellons, Nucl. Phys. B 563 (1999) 279 [hep-th/9905227] [INSPIRE].
  36. [36]
    J. Erdmenger and S. Lin, Thermalization from gauge/gravity duality: Evolution of singularities in unequal time correlators, JHEP 10 (2012) 028 [arXiv:1205.6873] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  37. [37]
    D. Galante and M. Schvellinger, Thermalization with a chemical potential from AdS spaces, JHEP 07 (2012) 096 [arXiv:1205.1548] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    E. Caceres and A. Kundu, Holographic Thermalization with Chemical Potential, JHEP 09 (2012) 055 [arXiv:1205.2354] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    W. Baron, D. Galante and M. Schvellinger, Dynamics of holographic thermalization, JHEP 03 (2013) 070 [arXiv:1212.5234] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    V. Keranen, E. Keski-Vakkuri and L. Thorlacius, Thermalization and entanglement following a non-relativistic holographic quench, Phys. Rev. D 85 (2012) 026005 [arXiv:1110.5035] [INSPIRE].
  41. [41]
    M. Alishahiha, A. Faraji Astaneh and M.R. Mohammadi Mozaffar, Thermalization in backgrounds with hyperscaling violating factor, Phys. Rev. D 90 (2014) 046004 [arXiv:1401.2807] [INSPIRE].
  42. [42]
    P. Fonda, L. Franti, V. Keränen, E. Keski-Vakkuri, L. Thorlacius and E. Tonni, Holographic thermalization with Lifshitz scaling and hyperscaling violation, JHEP 08 (2014) 051 [arXiv:1401.6088] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    I. Ya. Aref’eva, Formation time of quark-gluon plasma in heavy-ion collisions in the holographic shock wave model, Teor. Mat. Fiz. 184 (2015) 398 [arXiv:1503.02185] [INSPIRE].
  44. [44]
    I. Ya. Aref’eva, A.A. Golubtsova and E. Gourgoulhon, Analytic black branes in Lifshitz-like backgrounds and thermalization, JHEP 09 (2016) 142 [arXiv:1601.06046] [INSPIRE].
  45. [45]
    I. Ya. Aref’eva and I. Volovich, Holographic Photosynthesis, arXiv:1603.09107 [INSPIRE].
  46. [46]
    K. Landsteiner, E. Lopez and G. Milans del Bosch, Quenching the Chiral Magnetic Effect via the Gravitational Anomaly and Holography, Phys. Rev. Lett. 120 (2018) 071602 [arXiv:1709.08384] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    M.J. Bhaseen, B. Doyon, A. Lucas and K. Schalm, Far from equilibrium energy flow in quantum critical systems, Nature Phys. 11 (2015) 5 [arXiv:1311.3655] [INSPIRE].zbMATHGoogle Scholar
  48. [48]
    J. Erdmenger, D. Fernandez, M. Flory, E. Megias, A.-K. Straub and P. Witkowski, Time evolution of entanglement for holographic steady state formation, JHEP 10 (2017) 034 [arXiv:1705.04696] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  49. [49]
    V.E. Hubeny, M. Rangamani and E. Tonni, Thermalization of Causal Holographic Information, JHEP 05 (2013) 136 [arXiv:1302.0853] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  50. [50]
    V. Ziogas, Holographic mutual information in global Vaidya-BTZ spacetime, JHEP 09 (2015) 114 [arXiv:1507.00306] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  51. [51]
    S. Kundu and J.F. Pedraza, Spread of entanglement for small subsystems in holographic CFTs, Phys. Rev. D 95 (2017) 086008 [arXiv:1602.05934] [INSPIRE].
  52. [52]
    P. Calabrese and J.L. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech. 0504 (2005) P04010 [cond-mat/0503393] [INSPIRE].
  53. [53]
    P. Calabrese and J.L. Cardy, Time-dependence of correlation functions following a quantum quench, Phys. Rev. Lett. 96 (2006) 136801 [cond-mat/0601225] [INSPIRE].
  54. [54]
    S. Sotiriadis, P. Calabrese and J. Cardy, Quantum Quench from a Thermal Initial State, Europhys. Lett. 87 (2009) 20002 [arXiv:0903.0895].ADSCrossRefGoogle Scholar
  55. [55]
    H. Casini, H. Liu and M. Mezei, Spread of entanglement and causality, JHEP 07 (2016) 077 [arXiv:1509.05044] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  56. [56]
    M. Mezei, On entanglement spreading from holography, JHEP 05 (2017) 064 [arXiv:1612.00082] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  57. [57]
    J. Cardy, Quantum Quenches to a Critical Point in One Dimension: some further results, J. Stat. Mech. 1602 (2016) 023103 [arXiv:1507.07266] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  58. [58]
    V. Balasubramanian, A. Bernamonti, J. de Boer, B. Craps, L. Franti, F. Galli et al., Inhomogeneous holographic thermalization, JHEP 10 (2013) 082 [arXiv:1307.7086] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    L. McGough, M. Mezei and H. Verlinde, Moving the CFT into the bulk with \( T\overline{T} \), arXiv:1611.03470 [INSPIRE].
  60. [60]
    I. Ya. Aref’eva, M.A. Khramtsov and M.D. Tikhanovskaya, Thermalization after holographic bilocal quench, JHEP 09 (2017) 115 [arXiv:1706.07390] [INSPIRE].
  61. [61]
    M. Nozaki, T. Numasawa and T. Takayanagi, Holographic Local Quenches and Entanglement Density, JHEP 05 (2013) 080 [arXiv:1302.5703] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

Personalised recommendations