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

TL;DR

This paper investigates non-equilibrium dynamics and entanglement entropy in 2D holographic superconductors using gauge-string duality, employing numerical methods to analyze time-dependent fields and phase transitions.

Contribution

It introduces a numerical approach to study time-dependent scalar and Maxwell fields in 2D holographic superconductors, revealing insights into their non-equilibrium behavior and entanglement entropy.

Findings

Exponential decay of Maxwell field on AdS horizon characterized by parameter b.

Discontinuity in entanglement entropy derivative as conserved charge J increases.

System tends toward equilibrium over long time intervals.

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 $AdS_3$ 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.