### Abstract

We study the non-equilibrium condensation process in the 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.

Original language | English |
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Title of host publication | Proceedings of the 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010 |

Pages | 217-222 |

Number of pages | 6 |

Publication status | Published - 2010 |

Externally published | Yes |

Event | 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010 - Kyoto, Japan Duration: 2010 Sep 21 → 2010 Sep 25 |

### Other

Other | 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010 |
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Country | Japan |

City | Kyoto |

Period | 10/9/21 → 10/9/25 |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Proceedings of the 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010*(pp. 217-222)

**Non-equilibrium condensation process in a holographic superconductor.** / Kinoshita, Shunichiro; Murata, Keiju; Tanahashi, Norihiro.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010.*pp. 217-222, 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010, Kyoto, Japan, 10/9/21.

}

TY - GEN

T1 - Non-equilibrium condensation process in a holographic superconductor

AU - Kinoshita, Shunichiro

AU - Murata, Keiju

AU - Tanahashi, Norihiro

PY - 2010

Y1 - 2010

N2 - We study the non-equilibrium condensation process in the holographic superconductor. When the temperature T is smaller than a critical temperature Tc, 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 < Tc, 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.

AB - We study the non-equilibrium condensation process in the holographic superconductor. When the temperature T is smaller than a critical temperature Tc, 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 < Tc, 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.

UR - http://www.scopus.com/inward/record.url?scp=84887423806&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887423806&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84887423806

SP - 217

EP - 222

BT - Proceedings of the 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010

ER -