Non-equilibrium phase and entanglement entropy in 2D holographic superconductors via gauge-string duality

An alternative method of developing the theory of non-equilibrium two-dimensional holographic superconductor is to start from the definition of a time-dependent AdS₃ 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 behavior 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 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 ψ(z, t) near the AdS boundary. It may be possible that a long interval would elapse in the system, which tends to the equilibrium state, where 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 area, we find a discontinuity in the first derivative of the entanglement entropy as the conserved charge J is increased.