Abstract
We study the non-equilibrium condensation process in a holographic superconductor. When the temperature T is smaller than a critical temperature T c , there are two black hole solutions, the Reissner-Nordström-AdS black hole and a black hole with a scalar hair. In the boundary theory, they can be regarded as the supercooled normal phase and the superconducting phase, respectively. We consider perturbations on supercooled Reissner-Nordström-AdS black holes and study their non-linear time evolution to know about physical phenomena associated with rapidly-cooled superconductors. We find that, for T < T c , the initial perturbations grow exponentially and, eventually, spacetimes approach the hairy black holes. We also clarify how the relaxation process from a far-from-equilibrium state proceeds in the boundary theory by observing the time dependence of the superconducting order parameter. Finally, we study the time evolution of event and apparent horizons and discuss their correspondence with the entropy of the boundary theory. Our result gives a first step toward the holographic understanding of the non-equilibrium process in superconductors.
Similar content being viewed by others
References
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] [SPIRES].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].
S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [SPIRES].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [SPIRES].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [SPIRES].
M. Mondello and N. Goldenfeld, Scaling and vortex dynamics after the quench of a system with a continuous symmetry, Phys. Rev. A 42 (1990) 5865 [SPIRES].
F. Liu, M. Mondello and N. Goldenfeld, Kinetics of the superconducting transition, Phys. Rev. Lett. 66 (1991) 3071 [SPIRES].
M. Mondello and N. Goldenfeld, Scaling and vortex-string dynamics in a three-dimensional system with a continuous symmetry, Phys. Rev. A 45 (1992) 657 [SPIRES].
M. Mondello and N. Goldenfeld, Scaling and vortex-string dynamics in a three-dimensional system with a continuous symmetry, Phys. Rev. A 45 (1992) 657 [SPIRES].
G.J. Stephens, L.M.A. Bettencourt and W.H. Zurek, Critical dynamics of gauge systems: Spontaneous vortex formation in 2D superconductors, Phys. Rev. Lett. 88 (2002) 137004 [cond-mat/0108127] [SPIRES].
R.A. Janik and R.B. Peschanski, Asymptotic perfect fluid dynamics as a consequence of AdS/CFT, Phys. Rev. D 73 (2006) 045013 [hep-th/0512162] [SPIRES].
P. Kovtun, D.T. Son and A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [SPIRES].
S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [SPIRES].
D. Grumiller and P. Romatschke, On the collision of two shock waves in AdS5, JHEP 08 (2008) 027 [arXiv:0803.3226] [SPIRES].
S.S. Gubser, S.S. Pufu and A. Yarom, Entropy production in collisions of gravitational shock waves and of heavy ions, Phys. Rev. D 78 (2008) 066014 [arXiv:0805.1551] [SPIRES].
L. Alvarez-Gaumè, C. Gomez, A. Sabio Vera, A. Tavanfar and M.A. Vazquez-Mozo, Critical formation of trapped surfaces in the collision of gravitational shock waves, JHEP 02 (2009) 009 [arXiv:0811.3969] [SPIRES].
S. Lin and E. Shuryak, Grazing Collisions of Gravitational Shock Waves and Entropy Production in Heavy Ion Collision, Phys. Rev. D 79 (2009) 124015 [arXiv:0902.1508] [SPIRES].
S.S. Gubser, S.S. Pufu and A. Yarom, Off-center collisions in AdS 5 with applications to multiplicity estimates in heavy-ion collisions, JHEP 11 (2009) 050 [arXiv:0902.4062] [SPIRES].
S. Bhattacharyya and S. Minwalla, Weak Field Black Hole Formation in Asymptotically AdS Spacetimes, JHEP 09 (2009) 034 [arXiv:0904.0464] [SPIRES].
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] [SPIRES].
I. Amado, M. Kaminski and K. Landsteiner, Hydrodynamics of Holographic Superconductors, JHEP 05 (2009) 021 [arXiv:0903.2209] [SPIRES].
R.A. Konoplya and A. Zhidenko, Holographic conductivity of zero temperature superconductors, Phys. Lett. B 686 (2010) 199 [arXiv:0909.2138] [SPIRES].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [SPIRES].
G.T. Horowitz, Introduction to Holographic Superconductors, arXiv:1002.1722 [SPIRES].
K. Maeda, M. Natsuume and T. Okamura, Universality class of holographic superconductors, Phys. Rev. D 79 (2009) 126004 [arXiv:0904.1914] [SPIRES].
P. Basu, A. Mukherjee and H.H. Shieh, Supercurrent: Vector Hair for an AdS Black Hole, Phys. Rev. D 79 (2009) 045010 [arXiv:0809.4494] [SPIRES].
C.P. Herzog, P.K. Kovtun and D.T. Son, Holographic model of superfluidity, Phys. Rev. D 79 (2009) 066002 [arXiv:0809.4870] [SPIRES].
C.P. Herzog and A. Yarom, Sound modes in holographic superfluids, Phys. Rev. D 80 (2009) 106002 [arXiv:0906.4810] [SPIRES].
K. Maeda, S. Fujii and J.-i. Koga, The final fate of instability of Reissner-Nordstróm-anti-de Sitter black holes by charged complex scalar fields, Phys. Rev. D 81 (2010) 124020 [arXiv:1003.2689] [SPIRES].
R.A. Konoplya, Decay of charged scalar field around a black hole: Quasinormal modes of R-N, R-N-AdS and dilaton black hole, Phys. Rev. D 66 (2002) 084007 [gr-qc/0207028] [SPIRES].
A.S. Miranda, J. Morgan and V.T. Zanchin, Quasinormal modes of plane-symmetric black holes according to the AdS/CFT correspondence, JHEP 11 (2008) 030 [arXiv:0809.0297] [SPIRES].
S. Bhattacharyya et al., Local Fluid Dynamical Entropy from Gravity, JHEP 06 (2008) 055 [arXiv:0803.2526] [SPIRES].
S. Kinoshita, S. Mukohyama, S. Nakamura and K.-y. Oda, A Holographic Dual of Bjorken Flow, Prog. Theor. Phys. 121 (2009) 121 [arXiv:0807.3797] [SPIRES].
P. Figueras, V.E. Hubeny, M. Rangamani and S.F. Ross, Dynamical black holes and expanding plasmas, JHEP 04 (2009) 137 [arXiv:0902.4696] [SPIRES].
S.R. Das, T. Nishioka and T. Takayanagi, Probe Branes, Time-dependent Couplings and Thermalization in AdS/CFT, arXiv:1005.3348 [SPIRES].
C. Wu, K. Sun, E. Fradkin and S.-C. Zhang, Fermi liquid instabilities in the spin channel, Phys. Rev. B 75 (2007) 115103 [SPIRES].
J.-W. Chen, Y.-J. Kao and W.-Y. Wen, Peak-Dip-Hump from Holographic Superconductivity, arXiv:0911.2821 [SPIRES].
T. Faulkner, G.T. Horowitz, J. McGreevy, M.M. Roberts and D. Vegh, Photoemission ’experiments’ on holographic superconductors, JHEP 03 (2010) 121 [arXiv:0911.3402] [SPIRES].
S.S. Gubser, F.D. Rocha and P. Talavera, Normalizable fermion modes in a holographic superconductor, arXiv:0911.3632 [SPIRES].
T. Hartman and S.A. Hartnoll, Cooper pairing near charged black holes, JHEP 06 (2010) 005 [arXiv:1003.1918] [SPIRES].
Y.M. Galperin, V.L. Gurevich, V.I. Kozub and A.L. Shelankov, Theory of thermoelectric phenomena in superconductors, Phys. Rev. B 65 (2002) 064531.
O. Ozen and R. Narayanan, The physics of evaporative and convective instabilities in bilayer systems: Linear theory, Phys. Fluids 16 (2004) 4644.
O. Ozen and R. Narayanan, The physics of evaporative instability in bilayer systems: Weak nonlinear theory, Phys. Fluids 16 (2004) 4653.
T. Albash and C.V. Johnson, Vortex and Droplet Engineering in Holographic Superconductors, Phys. Rev. D 80 (2009) 126009 [arXiv:0906.1795] [SPIRES].
M. Montull, A. Pomarol and P.J. Silva, The Holographic Superconductor Vortex, Phys. Rev. Lett. 103 (2009) 091601 [arXiv:0906.2396] [SPIRES].
H. Yoshino and M. Shibata, Higher-dimensional numerical relativity: Formulation and code tests, Phys. Rev. D 80 (2009) 084025 [arXiv:0907.2760] [SPIRES].
K.-i. Nakao, H. Abe, H. Yoshino and M. Shibata, Maximal slicing of D-dimensional spherically-symmetric vacuum spacetime, Phys. Rev. D 80 (2009) 084028 [arXiv:0908.0799] [SPIRES].
M. Shibata and H. Yoshino, Nonaxisymmetric instability of rapidly rotating black hole in five dimensions, Phys. Rev. D 81 (2010) 021501 [arXiv:0912.3606] [SPIRES].
M. Zilhao et al., Numerical relativity for D dimensional axially symmetric space-times: formalism and code tests, Phys. Rev. D 81 (2010) 084052 [arXiv:1001.2302] [SPIRES].
H. Witek et al., Black holes in a box: towards the numerical evolution of black holes in AdS, J. Phys. Conf. Ser. 229 (2010) 012072 [arXiv:1004.4633] [SPIRES].
K. Maeda, M. Natsuume and T. Okamura, Vortex lattice for a holographic superconductor, Phys. Rev. D 81 (2010) 026002 [arXiv:0910.4475] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1005.0633
Rights and permissions
About this article
Cite this article
Murata, K., Kinoshita, S. & Tanahashi, N. Non-equilibrium condensation process in a holographic superconductor. J. High Energ. Phys. 2010, 50 (2010). https://doi.org/10.1007/JHEP07(2010)050
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2010)050