Non-equilibrium phase and entanglement entropy in 2D holographic superconductors via Gauge-String duality

Abstract

An alternative method of developing the theory of non-equilibrium two dimensional holographic superconductor is to start from the definition of a time dependent $Ad{S}_3$ background. As originally proposed, many of these formulae were cast in exponential form, but the adoption of the numeric method of expression throughout the bulk serves to show more clearly the relationship between the various parameters. The time dependence behaviour of the scalar condensation and Maxwell fields are fitted numerically. A usual value for Maxwell field on AdS horizon is $\exp (-bt)$, and the exponential $\log$ ratio is therefore $10^{-8}{s}^{-1}$. The coefficient $b$ of the time in the exponential term $\exp (-bt)$ can be interpreted as a tool to measure the degree of dynamical instability, its reciprocal $\frac{1}{b}$ is the time in which the disturbance is multiplied in the ratio. A discussion of some of the exponential formulae is given by the scalar field $\psi (z,t)$ near the AdS boundary. It might be possible that a long interval would elapse the system which tends to the equilibrium state when the normal mass and conformal dimensions emerged. A somewhat curious calculation has been made, to illustrate the holographic entanglement entropy for this system. The foundation of all this calculation is, of course, a knowledge of multiple (connected and disconnected) extremal surfaces. There are several cases in which exact and approximate solutions are jointly used, a variable numerical quantity is represented by a graph, and the principles of approximation are then applied to determine related numerical quantities. In the case of the disconnected phase with a finite extremal are, we find a discontinuity in the first derivative of the entanglement entropy as the conserved charge $J$ is increased.

References in corpus (15)

• Building an AdS/CFT superconductor
• Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma
• Thermalization of Strongly Coupled Field Theories
• Thermodynamical Property of Entanglement Entropy for Excited States
• Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches
• A numerical relativity approach to the initial value problem in asymptotically Anti-de Sitter spacetime for plasma thermalization - an ADM formulation
• Non-equilibrium Condensation Process in a Holographic Superconductor
• Dynamics of holographic thermalization
• On entanglement entropy functionals in higher derivative gravity theories
• Holographic Entanglement Entropy of Multiple Strips
• Holographic entanglement entropy in general holographic superconductor models
• Holographic Entanglement Entropy in 2D Holographic Superconductor via $Ad{S}_3/CF{T}_2$
• Renormalization group flow of entanglement entropy on spheres
• 1+1-dimensional p-wave superconductors from intersecting D-branes
• Renormalized Entanglement Entropy for BPS Black Branes