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A Thermal Quench Induces Spatial Inhomogeneities in a Holographic Superconductor

A Thermal Quench Induces Spatial Inhomogeneities in a Holographic Superconductor. Hai -Qing Zhang ( Instituto Superior Técnico , Lisboa ) INI, Cambridge, 17/09/2013 Coauthor: Antonio M. García-García & Hua -Bi Zeng , arXiv:1308.5398 . Introduction.

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A Thermal Quench Induces Spatial Inhomogeneities in a Holographic Superconductor

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  1. A Thermal Quench Induces Spatial Inhomogeneities in a Holographic Superconductor Hai-Qing Zhang (Instituto Superior Técnico, Lisboa) INI, Cambridge, 17/09/2013 Coauthor: Antonio M. García-García & Hua-Bi Zeng, arXiv:1308.5398

  2. Introduction • Static homogeneous holographic superconductor (HSC) • Dynamical homogeneous HSC • Static inhomogeneous HSC

  3. Gubser, Phys. Rev. D 78 (2008) 065034 • Static homogeneous HSC: • Einstein-Maxwell-charged scalar action with negative cosmological constant • T>Tc (or μ< μc, since T~1/ μ): ψ=0; T<Tc : two available solutions ψ=0 ψ≠0 Hartnoll, Herzog, & Horowtiz, Phys.Rev.Lett. 101 (2008) 031601 superconducting solution free energy

  4. Murata, Kinoshita & Tanahashi, JHEP 1007 (2010) 050  Gaussian quench • Dynamical homogeneous HSC after a quench: T<Tc, RN-AdS static hairy black hole; normal phase superconducting phase

  5. Bhaseen, Gauntlett, Simons, Sonner & Wiseman, Phys.Rev.Lett. 110 (2013) 015301 three kinds of decays are found, consistent with QNMs

  6. Gao, Garcia-Garcia, Zeng & Zhang:arXiv:1212.1049 AdSsoliton background, undamped oscillation modes are found; lack of thermalization in CFT

  7. Polkovnikov, Sengupta, Silva, Vengalattore, Rev.Mod.Phys. 83 (2011) 863  CMT: lack of thermalization comes from integrability. Question: what is the relation between a gravity without horizon and the integrable field theory on boundary?

  8. Flauger, Pajer & Papanikolaou, Phys.Rev. D83 (2011) 064009  • Static inhomogeneous HSC: Einstein- Maxwell-scalar action, modulated chemical potential, striped superconductor, explicitly break translational symmetry, free energy is lower than the homogeneous case

  9. Donos & Gauntlett, JHEP 1108, 140 (2011) Rozali, Smyth, Sorkin & Stang, Phys.Rev.Lett. 110, (2013) 201603   Einstein-Maxwell-axion action, spontaneously break the translational symmetry, striped order parameter

  10. Liu, Ooguri, Stoica & Yunes, Phys. Rev. Lett. 110, (2013) 211601 Chern-Simons term , spontaneously generate angular momentum

  11. Other references: • dynamical studies : • inhomogeneous studies: I. Amado, M. Kaminski & K. Landsteiner, JHEP, 0905021 (2009) S. Bhattacharyya, and S. Minwalla, JHEP 0909:034, (2009) P. Bizon, and A. Rostworowski, Phys. Rev. Lett. 107, 031102 (2011) O. Dias, G. Horowitz, D. Marolf and J. Santos, Class. Quant. Grav. 29, 235019 (2012) P. Basu, D. Das, S. Das and T. Nishioka, arXiv:1211.7076 … S. Nakamura, H. Ooguri and C. -S. Park, Phys. Rev. D 81, 044018 (2010) G. T. Horowitz, J. E. Santos and D. Tong, JHEP 1211, 102 (2012) …

  12. Motivation to Dynamical Inhomogeneous HSC • Kibble-Zurek mechanisms: topological defects generated from a sudden quench Zel’dovich, Kobzarev & Okun, Zh. eksp. teor. Fiz. 67, 3 (1974); Soviet Phys. JETP 67, 401 (1975) Kibble, J. Phys. A 9, 1387 (1976) Zurek, Nature 317, 505 (1985)

  13. Dzero, Yuzbashyan & Altshuler, Eur. Phys. Lett. 85 (2009) 20004 system size larger than superconducting coherence length, quench can excite finite momentum states, results in spatial inhomogeneities

  14. Donos & Gauntlett, JHEP 1108, 140 (2011) Rozali, Smyth, Sorkin & Stang, Phys.Rev.Lett. 110, (2013) 201603   • From holography: • axion fields, spontaneously break the translational symmetry. • angular momentum generation from Chern-Simons terms. • How about a quench depending on time? Liu, Ooguri, Stoica & Yunes, Phys. Rev. Lett. 110, (2013) 211601

  15. Dynamical inhomogeneous HSC • Einstein-Maxwell-complex scalar action: in which • AdS-Schwarzschild black hole: with

  16. Fields depend on t,r & x. • Ansatz: • 4 independent EoMs, 1 constraint equation • Boundary conditions: • At horizon: Mt(t, x)|rh=0; • Other fields are finite

  17. For m^2=-2, expansions near boundary: -charge density; -chemical potential; source ; order parameter - superfluid velocity; supercurrent

  18. Thermal quench, since T~1/, it is equal to quench chemical potential. • Quench A: i=4.5, f=4.8, corresponding to Ti=0.903Tc, Tf=0.846Tc since for homogeneous case c=4.063 (m^2=-2) Hartnoll, Herzog, & Horowtiz, Phys.Rev.Lett. 101 (2008) 031601

  19. chemical potential expectation value

  20. t=30 t=9.7 t=1.2 t=0 oscillations in time inhomogeneous order parameter Physical meaning: quench will excite finite momentum

  21. Quench B: i=5.5, f=5.8, corresponding to Ti=0.738 Tc, Tf=0.700 Tc. chemical potential expectation value

  22. Free energy, grand canonical ensemble, F=-TSos where z=1/r, h=1-z^3

  23. quench A • at late times quench B

  24. Summaries • Developments in HSC: static homogeneous, dynamical homogeneous, static inhomogeneous. • Motivation: spontaneous symmetry breaking • Dynamical inhomogeneous HSC, a quench induces translational symmetry breaking

  25. Thanks for your attention!

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