Normal modes and time evolution of a holographic superconductor after a quantum quench

  • Xin Gao
  • Antonio M. García-García
  • Hua Bi Zeng
  • Hai-Qing Zhang
Open Access
Article

Abstract

We employ holographic techniques to investigate the dynamics of the order parameter of a strongly coupled superconductor after a perturbation that drives the system out of equilibrium. The gravity dual that we employ is the AdS5 Soliton background at zero temperature. We first analyze the normal modes associated to the superconducting order parameter which are purely real since the background has no horizon. We then study the full time evolution of the order parameter after a quench. For sufficiently a weak and slow perturbation we show that the order parameter undergoes simple undamped oscillations in time with a frequency that agrees with the lowest normal model computed previously. This is expected as the soliton background has no horizon and therefore, at least in the probe and large N limits considered, the system will never return to equilibrium. For stronger and more abrupt perturbations higher normal modes are excited and the pattern of oscillations becomes increasingly intricate. We identify a range of parameters for which the time evolution of the order parameter become quasi chaotic. The details of the chaotic evolution depend on the type of perturbation used. Therefore it is plausible to expect that it is possible to engineer a perturbation that leads to the almost complete destruction of the oscillating pattern and consequently to quasi equilibration induced by superposition of modes with different frequencies.

Keywords

Gauge-gravity correspondence 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.

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Xin Gao
    • 1
    • 2
  • Antonio M. García-García
    • 3
    • 4
  • Hua Bi Zeng
    • 4
    • 5
  • Hai-Qing Zhang
    • 4
  1. 1.Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)MünchenGermany
  2. 2.State Key Laboratory of Theoretical PhysicsInstitute of Theoretical Physics, Chinese Academy of SciencesBeijingChina
  3. 3.University of Cambridge, Cavendish LaboratoryCambridgeU.K.
  4. 4.CFIF, Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal
  5. 5.School of Mathematics and PhysicsBohai UniversityJinZhouChina

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