Skip to main content
SpringerLink
Log in

Quantum quenches of holographic plasmas

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

Abstract

We employ holographic techniques to study quantum quenches at finite temperature, where the quenches involve varying the coupling of the boundary theory to a relevant operator with an arbitrary conformal dimension 2 ≤ Δ ≤ 4. The dual bulk theory is five-dimensional Einstein gravity with negative cosmological constant coupled to a massive real scalar and our calculations are perturbative in the amplitude of the bulk scalar. The evolution of the system is studied by evaluating the expectation value of the quenched operator and the stress tensor throughout the process. The time dependence of the new coupling is characterized by a fixed timescale and the response of the observables depends on the ratio of the this timescale to the initial temperature. The observables exhibit universal scaling behaviours when the transitions are either fast or slow, i.e., when this ratio is very small or very large. The scaling exponents are smooth functions of the operator dimension. We find that in fast quenches, the relaxation time is set by the thermal timescale regardless of the operator dimension or the precise quenching rate.

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. S. Mondal, D. Sen and K. Sengupta, Non-equilibrium dynamics of quantum systems: order parameter evolution, defect generation, and qubit transfer, Quantum Quenching, Anealing and Computation, Lect. Notes Phys. 802 (2010) 21 [arXiv:0908.2922].

    Article  ADS  Google Scholar 

  2. J. Dziarmaga, Dynamics of a quantum phase transition and relaxation to a steady state, Adv. Phys. 59 (2010) 1063 [arXiv:0912.4034].

    Article  ADS  Google Scholar 

  3. A. Polkovnikov, K. Sengupta, A. Silva and M. Vengalattore, Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys. 83 (2011) 863 [arXiv:1007.5331] [INSPIRE].

    Article  ADS  Google Scholar 

  4. A. Lamacraft and J. Moore, Potential insights into non-equilibrium behavior from atomic physics, chapter forthcoming in Ultracold Bosonic and Fermionic Gases, A. Fletcher, K. Levin and D. Stamper-Kurn eds., Contemporary Concepts in Condensed Matter Science, Elsevier, The Netherlands (2012) [arXiv:1106.3567].

  5. L.D. Landau and E.M. Lifshitz, Quantum mechanics, Course of Theoretical Physics, Volume 3, (1989).

  6. P. Calabrese and J.L. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech. 04 (2005) P04010 [cond-mat/0503393] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  7. 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].

    Article  ADS  Google Scholar 

  8. P. Calabrese and J. Cardy, Quantum quenches in extended systems, J. Stat. Mech. 06 (2007) P06008 [arXiv:0704.1880] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  9. S. Sotiriadis and J. Cardy, Quantum quench in interacting field theory: a self-consistent approximation, Phys. Rev. B 81 (2010) 134305 [arXiv:1002.0167] [INSPIRE].

    ADS  Google Scholar 

  10. S. Sotiriadis and J. Cardy, Inhomogeneous quantum quenches, J. Stat. Mech. 11 (2008) P11003 [arXiv:0808.0116].

    Article  Google Scholar 

  11. S. Sotiriadis, P. Calabrese and J. Cardy, Quantum quench from a thermal initial state, EPL 87 (2009) 20002 [arXiv:0903.0895].

    Article  ADS  Google Scholar 

  12. M. Rigol, V. Dunjko, V. Yurovsky and M. Olshanii, Relaxation in a completely integrable many-body quantum system: an ab initio study of the dynamics of the highly excited states of lattice hard-core bosons, Phys. Rev. Lett. 98 (2006) 050405.

    Article  Google Scholar 

  13. C. Kollath, A.M. Läuchli and E. Altman, Quench dynamics and nonequilibrium phase diagram of the Bose-Hubbard model, Phys. Rev. Lett. 98 (2007) 180601 [cond-mat/0607235].

    Article  ADS  Google Scholar 

  14. S.R. Manmana, S. Wessel, R.M. Noack and A. Muramatsu, Strongly correlated fermions after a quantum quench, Phys. Rev. Lett. 98 (2007) 210405 [cond-mat/0612030].

    Article  ADS  Google Scholar 

  15. L.-Y. Hung, M. Smolkin and E. Sorkin, Modification of late time phase structure by quantum quenches, Phys. Rev. Lett. 109 (2012) 155702 [arXiv:1206.2685] [INSPIRE].

    Article  ADS  Google Scholar 

  16. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].

    MathSciNet  ADS  MATH  Google Scholar 

  17. O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. S.R. Das, T. Nishioka and T. Takayanagi, Probe branes, time-dependent couplings and thermalization in AdS/CFT, JHEP 07 (2010) 071 [arXiv:1005.3348] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. P. Basu and S.R. Das, Quantum quench across a holographic critical point, JHEP 01 (2012) 103 [arXiv:1109.3909] [INSPIRE].

    Article  ADS  Google Scholar 

  20. S.R. Das, Holographic quantum quench, J. Phys. Conf. Ser. 343 (2012) 012027 [arXiv:1111.7275] [INSPIRE].

    Article  ADS  Google Scholar 

  21. P. Basu, D. Das, S.R. Das and T. Nishioka, Quantum quench across a zero temperature holographic superfluid transition, JHEP 03 (2013) 146 [arXiv:1211.7076] [INSPIRE].

    Article  ADS  Google Scholar 

  22. 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].

    Article  MathSciNet  ADS  Google Scholar 

  23. 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].

    Article  MathSciNet  ADS  Google Scholar 

  24. S.B. Giddings and S.F. Ross, D3-brane shells to black branes on the Coulomb branch, Phys. Rev. D 61 (2000) 024036 [hep-th/9907204] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  25. S.B. Giddings and A. Nudelman, Gravitational collapse and its boundary description in AdS, JHEP 02 (2002) 003 [hep-th/0112099] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. S. Bhattacharyya and S. Minwalla, Weak field black hole formation in asymptotically AdS spacetimes, JHEP 09 (2009) 034 [arXiv:0904.0464] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. R.A. Janik and R.B. Peschanski, Gauge/gravity duality and thermalization of a boost-invariant perfect fluid, Phys. Rev. D 74 (2006) 046007 [hep-th/0606149] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  28. R.A. Janik, Viscous plasma evolution from gravity using AdS/CFT, Phys. Rev. Lett. 98 (2007) 022302 [hep-th/0610144] [INSPIRE].

    Article  ADS  Google Scholar 

  29. S. Lin and E. Shuryak, Toward the AdS/CFT gravity dual for high energy collisions. 3. Gravitationally collapsing shell and quasiequilibrium, Phys. Rev. D 78 (2008) 125018 [arXiv:0808.0910] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  30. 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 

  31. 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].

    Article  ADS  Google Scholar 

  32. H. Ebrahim and M. Headrick, Instantaneous thermalization in holographic plasmas, arXiv:1010.5443 [INSPIRE].

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

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

  35. V. Balasubramanian, A. Bernamonti, N. Copland, B. Craps and F. Galli, Thermalization of mutual and tripartite information in strongly coupled two dimensional conformal field theories, Phys. Rev. D 84 (2011) 105017 [arXiv:1110.0488] [INSPIRE].

    ADS  Google Scholar 

  36. 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 

  37. A. Allais and E. Tonni, Holographic evolution of the mutual information, JHEP 01 (2012) 102 [arXiv:1110.1607] [INSPIRE].

    Article  ADS  Google Scholar 

  38. 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].

    ADS  Google Scholar 

  39. D. Galante and M. Schvellinger, Thermalization with a chemical potential from AdS spaces, JHEP 07 (2012) 096 [arXiv:1205.1548] [INSPIRE].

    Article  ADS  Google Scholar 

  40. E. Caceres and A. Kundu, Holographic thermalization with chemical potential, JHEP 09 (2012) 055 [arXiv:1205.2354] [INSPIRE].

    Article  ADS  Google Scholar 

  41. I.Y. Arefeva and I. Volovich, On holographic thermalization and dethermalization of quark-gluon plasma, arXiv:1211.6041 [INSPIRE].

  42. W. Baron, D. Galante and M. Schvellinger, Dynamics of holographic thermalization, JHEP 03 (2013) 070 [arXiv:1212.5234] [INSPIRE].

    Article  ADS  Google Scholar 

  43. P.M. Chesler and L.G. Yaffe, Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 102 (2009) 211601 [arXiv:0812.2053] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  44. P.M. Chesler and L.G. Yaffe, Boost invariant flow, black hole formation and far-from-equilibrium dynamics in N = 4 supersymmetric Yang-Mills theory, Phys. Rev. D 82 (2010) 026006 [arXiv:0906.4426] [INSPIRE].

    ADS  Google Scholar 

  45. D. Garfinkle and L.A. Pando Zayas, Rapid thermalization in field theory from gravitational collapse, Phys. Rev. D 84 (2011) 066006 [arXiv:1106.2339] [INSPIRE].

    ADS  Google Scholar 

  46. D. Garfinkle, L.A. Pando Zayas and D. Reichmann, On field theory thermalization from gravitational collapse, JHEP 02 (2012) 119 [arXiv:1110.5823] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  47. H. Bantilan, F. Pretorius and S.S. Gubser, Simulation of asymptotically AdS 5 spacetimes with a generalized harmonic evolution scheme, Phys. Rev. D 85 (2012) 084038 [arXiv:1201.2132] [INSPIRE].

    ADS  Google Scholar 

  48. M.P. Heller, D. Mateos, W. van der Schee and D. Trancanelli, Strong coupling isotropization of non-Abelian plasmas simplified, Phys. Rev. Lett. 108 (2012) 191601 [arXiv:1202.0981] [INSPIRE].

    Article  ADS  Google Scholar 

  49. M.P. Heller, R.A. Janik and P. Witaszczyk, A numerical relativity approach to the initial value problem in asymptotically anti-de Sitter spacetime for plasma thermalization — an ADM formulation, Phys. Rev. D 85 (2012) 126002 [arXiv:1203.0755] [INSPIRE].

    ADS  Google Scholar 

  50. M. Bhaseen, J.P. Gauntlett, B. Simons, J. Sonner and T. Wiseman, Holographic superfluids and the dynamics of symmetry breaking, Phys. Rev. Lett. 110 (2013) 015301 [arXiv:1207.4194] [INSPIRE].

    Article  ADS  Google Scholar 

  51. B. Wu, On holographic thermalization and gravitational collapse of massless scalar fields, JHEP 10 (2012) 133 [arXiv:1208.1393] [INSPIRE].

    Article  ADS  Google Scholar 

  52. B. Wu, On holographic thermalization and gravitational collapse of tachyonic scalar fields, JHEP 04 (2013) 044 [arXiv:1301.3796] [INSPIRE].

    Article  ADS  Google Scholar 

  53. V. Cardoso et al., NR/HEP: roadmap for the future, Class. Quant. Grav. 29 (2012) 244001 [arXiv:1201.5118] [INSPIRE].

    Article  ADS  Google Scholar 

  54. A. Buchel, L. Lehner and R.C. Myers, Thermal quenches in N = 2∗ plasmas, JHEP 08 (2012) 049 [arXiv:1206.6785] [INSPIRE].

    Article  ADS  Google Scholar 

  55. 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].

    MathSciNet  MATH  Google Scholar 

  56. 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].

    MathSciNet  ADS  Google Scholar 

  57. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

    MathSciNet  ADS  MATH  Google Scholar 

  58. P. Breitenlohner and D.Z. Freedman, Positive energy in anti-de Sitter backgrounds and gauged extended supergravity, Phys. Lett. B 115 (1982) 197 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  59. P. Breitenlohner and D.Z. Freedman, Stability in gauged extended supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  60. L. Mezincescu and P. Townsend, Stability at a local maximum in higher dimensional anti-de Sitter space and applications to supergravity, Annals Phys. 160 (1985) 406 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  61. I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  62. A. Buchel et al., Holographic GB gravity in arbitrary dimensions, JHEP 03 (2010) 111 [arXiv:0911.4257] [INSPIRE].

    Article  ADS  Google Scholar 

  63. S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear fluid dynamics from gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].

    Article  ADS  Google Scholar 

  64. V.E. Hubeny, S. Minwalla and M. Rangamani, The fluid/gravity correspondence, chapter in Black holes in higher dimensions, G. Horowitz ed., Cambridge University Press, Cambridge U.K. (2012) [arXiv:1107.5780] [INSPIRE].

  65. R. Emparan, C.V. Johnson and R.C. Myers, Surface terms as counterterms in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 104001 [hep-th/9903238] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  66. M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  67. M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  68. M. Bianchi, D.Z. Freedman and K. Skenderis, How to go with an RG flow, JHEP 08 (2001) 041 [hep-th/0105276] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  69. C. Fefferman and C.R. Graham, Conformal invariants, in Elie Cartan et les Mathématiques d’aujourd hui, Astérisque, France (1985), pg. 95.

    Google Scholar 

  70. C. Fefferman and C.R. Graham, The ambient metric, arXiv:0710.0919 [INSPIRE].

  71. L.-Y. Hung, R.C. Myers and M. Smolkin, Some calculable contributions to holographic entanglement entropy, JHEP 08 (2011) 039 [arXiv:1105.6055] [INSPIRE].

    Article  ADS  Google Scholar 

  72. O. Aharony, A. Buchel and A. Yarom, Holographic renormalization of cascading gauge theories, Phys. Rev. D 72 (2005) 066003 [hep-th/0506002] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  73. I. Papadimitriou, Holographic renormalization of general dilaton-axion gravity, JHEP 08 (2011) 119 [arXiv:1106.4826] [INSPIRE].

    Article  ADS  Google Scholar 

  74. A. Buchel, N = 2∗ hydrodynamics, Nucl. Phys. B 708 (2005) 451 [hep-th/0406200] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  75. A. Buchel and J.T. Liu, Thermodynamics of the N = 2∗ flow, JHEP 11 (2003) 031 [hep-th/0305064] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  76. P.M. Hohler and M.A. Stephanov, Holography and the speed of sound at high temperatures, Phys. Rev. D 80 (2009) 066002 [arXiv:0905.0900] [INSPIRE].

    ADS  Google Scholar 

  77. R. Isaacson, J. Welling and J. Winicour, Null cone computation of gravitational radiation, J. Math. Phys. 24 (1983) 1824 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  78. L. Lehner, A dissipative algorithm for wave-like equations in the characteristic formulation, J. Comput. Phys. 149 (1999) 1 [gr-qc/9811095] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  79. A. Buchel, L. Lehner, R.C. Myers and A. van Niekerk, Universality of abrupt holographic quenches, in preparation.

Download references

Author information

Authors and Affiliations

  1. Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, N2J 2W9, Canada

    Alex Buchel, Luis Lehner, Robert C. Myers & Anton van Niekerk

  2. Department of Applied Mathematics, University of Western Ontario, 1151 Richmond Street, London, Ontario, N6A 5B7, Canada

    Alex Buchel

  3. Department of Physics & Astronomy and Guelph-Waterloo Physics Institute, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1, Canada

    Anton van Niekerk

Authors
  1. Alex Buchel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Luis Lehner
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Robert C. Myers
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Anton van Niekerk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anton van Niekerk.

Additional information

ArXiv ePrint: 1302.2924

Rights and permissions

Reprints and permissions

About this article

Cite this article

Buchel, A., Lehner, L., Myers, R.C. et al. Quantum quenches of holographic plasmas. J. High Energ. Phys. 2013, 67 (2013). https://doi.org/10.1007/JHEP05(2013)067

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP05(2013)067

Keywords

Search

Navigation