# Kibble-Zurek Scaling in a Holographic p-wave Superconductor

## TL;DR

This paper investigates the Kibble-Zurek mechanism in a 2D holographic p-wave superconductor, deriving and confirming the scaling laws of the Kibble-Zurek time through explicit holographic calculations.

## Contribution

It introduces a general scaling relation for the Kibble-Zurek time involving four critical exponents and confirms it within a holographic p-wave superconductor model.

## Key findings

- Confirmed the scaling of the Kibble-Zurek time in the model.
- Derived explicit scaling functions for the quench process.
- Found similarities with higher-dimensional s-wave superconductor quenches.

## Abstract

We study the Kibble-Zurek mechanism in a 2d holographic p-wave superconductor model with a homogeneous source quench on the critical point. We derive, on general grounds, the scaling of the Kibble-Zurek time, which marks breaking-down of adiabaticity. It is expressed in terms of four critical exponents, including three static and one dynamical exponents. Via explicit calculations within a holographic model, we confirm the scaling of the Kibble-Zurek time and obtain the scaling functions in the quench process. We find the results are formally similar to a homogeneous quench in a higher dimensional holographic s-wave superconductor. The similarity is due to the special type of quench we take. We expect differences in the quench dynamics if the condition of homogeneous source and dominance of critical mode are relaxed.