×
David, Justin R.; Khetrapal, Surbhi

Thermalization of Green functions and quasinormal modes. (English) Zbl 1388.83219

J. High Energy Phys. 2015, No. 7, Paper No. 41, 33 p. (2015).
Summary: We develop a new method to study the thermalization of time dependent retarded Green function in conformal field theories holographically dual to thin shell AdS Vaidya space times. The method relies on using the information of all time derivatives of the Green function at the shell and then evolving it for later times. The time derivatives of the Green function at the shell is given in terms of a recursion formula. Using this method we obtain analytic results for short time thermalization of the Green function. We show that the late time behaviour of the Green function is determined by the first quasinormal mode. We then implement the method numerically. As applications of this method we study the thermalization of the retarded time dependent Green function corresponding to a minimally coupled scalar in the \(\mathrm{AdS}_{3}\) and \(\mathrm{AdS}_{5}\) thin Vaidya shells. We see that as expected the late time behaviour is determined by the first quasinormal mode. We apply the method to study the late time behaviour of the shear vector mode in \(\mathrm{AdS}_{5}\) Vaidya shell. At small momentum the corresponding time dependent Green function is expected to relax to equilibrium by the shear hydrodynamic mode. Using this we obtain the universal ratio of the shear viscosity to entropy density from a time dependent process.

Cited in 7 Documents

MSC:

83C47 Methods of quantum field theory in general relativity and gravitational theory
83C57 Black holes
83E30 String and superstring theories in gravitational theory

Keywords:

gauge-gravity correspondence; black holes in string theory; AdS-CFT correspondence
PDF BibTeX XML Cite
\textit{J. R. David} and \textit{S. Khetrapal}, J. High Energy Phys. 2015, No. 7, Paper No. 41, 33 p. (2015; Zbl 1388.83219)
Full Text: DOI arXiv

References:

[1] B.V. Jacak and B. Müller, The exploration of hot nuclear matter, Science337 (2012) 310 [INSPIRE].
[2] M. Greiner, O. Mandel, T.W. Hänsch and I. Bloch, Collapse and revival of the matter wave field of a Bose-Einstein condensate, Nature419 (2002) 51 [cond-mat/0207196].
[3] A. Widera, F. Gerbier, S. Fölling, T. Gericke, O. Mandel and I. Bloch, Coherent collisional spin dynamics in optical lattices, Phys. Rev. Lett.95 (2005) 190405 [cond-mat/0505492].
[4] L.E. Sadler, J.M. Higbie, S.R. Leslie, M. Vengalattore and D.M. Stamper-Kurn, Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose-Einstein condensate, Nature443 (2006) 312 [cond-mat/0605351].
[5] T. Kinoshita, T. Wenger and D.S. Weiss, A quantum Newton’s cradle, Nature440 (2006) 900.
[6] S. Kalyana Rama and B. Sathiapalan, On the role of chaos in the AdS/CFT connection, Mod. Phys. Lett.A 14 (1999) 2635 [hep-th/9905219] [INSPIRE].
[7] 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]. · Zbl 0953.83038
[8] 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].
[9] U.H. Danielsson, E. Keski-Vakkuri and M. Kruczenski, Black hole formation in AdS and thermalization on the boundary, JHEP02 (2000) 039 [hep-th/9912209] [INSPIRE]. · Zbl 0959.83024
[10] S.B. Giddings and A. Nudelman, Gravitational collapse and its boundary description in AdS, JHEP02 (2002) 003 [hep-th/0112099] [INSPIRE].
[11] 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].
[12] 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].
[13] S. Bhattacharyya and S. Minwalla, Weak Field Black Hole Formation in Asymptotically AdS Spacetimes, JHEP09 (2009) 034 [arXiv:0904.0464] [INSPIRE].
[14] 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].
[15] G. Beuf, M.P. Heller, R.A. Janik and R. Peschanski, Boost-invariant early time dynamics from AdS/CFT, JHEP10 (2009) 043 [arXiv:0906.4423] [INSPIRE].
[16] M.P. Heller, R.A. Janik and P. Witaszczyk, The characteristics of thermalization of boost-invariant plasma from holography, Phys. Rev. Lett.108 (2012) 201602 [arXiv:1103.3452] [INSPIRE].
[17] 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].
[18] J. Abajo-Arrastia, J. Aparicio and E. Lopez, Holographic Evolution of Entanglement Entropy, JHEP11 (2010) 149 [arXiv:1006.4090] [INSPIRE]. · Zbl 1294.81128
[19] 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]. · Zbl 1448.83015
[20] H. Ebrahim and M. Headrick, Instantaneous Thermalization in Holographic Plasmas, arXiv:1010.5443 [INSPIRE].
[21] V. Balasubramanian et al., Holographic Thermalization, Phys. Rev.D 84 (2011) 026010 [arXiv:1103.2683] [INSPIRE].
[22] J. Aparicio and E. Lopez, Evolution of Two-Point Functions from Holography, JHEP12 (2011) 082 [arXiv:1109.3571] [INSPIRE]. · Zbl 1306.81145
[23] V. Balasubramanian et al., Thermalization of the spectral function in strongly coupled two dimensional conformal field theories, JHEP04 (2013) 069 [arXiv:1212.6066] [INSPIRE]. · Zbl 1342.81476
[24] N. Callebaut et al., Holographic Quenches and Fermionic Spectral Functions, JHEP10 (2014) 172 [arXiv:1407.5975] [INSPIRE]. · Zbl 1333.83036
[25] V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
[26] V. Keranen and P. Kleinert, Non-equilibrium scalar two point functions in AdS/CFT, JHEP04 (2015) 119 [arXiv:1412.2806] [INSPIRE]. · Zbl 1388.83277
[27] A. Núñez and A.O. Starinets, AdS/CFT correspondence, quasinormal modes and thermal correlators in N = 4 SYM, Phys. Rev.D 67 (2003) 124013 [hep-th/0302026] [INSPIRE].
[28] G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP09 (2002) 043 [hep-th/0205052] [INSPIRE].
[29] D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: Recipe and applications, JHEP09 (2002) 042 [hep-th/0205051] [INSPIRE].
[30] A. Buchel and J.T. Liu, Thermodynamics of the N = 2*flow, JHEP11 (2003) 031 [hep-th/0305064] [INSPIRE].
[31] D. Birmingham, Choptuik scaling and quasinormal modes in the AdS/CFT correspondence, Phys. Rev.D 64 (2001) 064024 [hep-th/0101194] [INSPIRE].
[32] D. Birmingham, I. Sachs and S.N. Solodukhin, Conformal field theory interpretation of black hole quasinormal modes, Phys. Rev. Lett.88 (2002) 151301 [hep-th/0112055] [INSPIRE].
[33] P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev.D 72 (2005) 086009 [hep-th/0506184] [INSPIRE].
[34] G.T. Horowitz and V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium, Phys. Rev.D 62 (2000) 024027 [hep-th/9909056] [INSPIRE].
[35] S.A. Stricker, Holographic thermalization in N = 4 Super Yang-Mills theory at finite coupling, Eur. Phys. J.C 74 (2014) 2727 [arXiv:1307.2736] [INSPIRE].
[36] S. Banerjee, R. Iyer and A. Mukhopadhyay, The holographic spectral function in non-equilibrium states, Phys. Rev.D 85 (2012) 106009 [arXiv:1202.1521] [INSPIRE].
[37] A. Mukhopadhyay, Nonequilibrium fluctuation-dissipation relation from holography, Phys. Rev.D 87 (2013) 066004 [arXiv:1206.3311] [INSPIRE].
[38] S. Datta and J.R. David, Higher Spin Quasinormal Modes and One-Loop Determinants in the BTZ black Hole, JHEP03 (2012) 079 [arXiv:1112.4619] [INSPIRE]. · Zbl 1309.81214
[39] S. Datta and J.R. David, Higher spin fermions in the BTZ black hole, JHEP07 (2012) 079 [arXiv:1202.5831] [INSPIRE]. · Zbl 1309.81214
[40] 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].
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.