# Universal scaling of conserved charge in the stochastic diffusion dynamics

## TL;DR

This paper investigates the universal scaling behavior of conserved charges during stochastic diffusion near critical points, revealing scale-invariant functions that are robust against initial conditions and model parameters.

## Contribution

It introduces universal functions for correlation and cumulant of conserved charges in critical regimes, derived from stochastic diffusion dynamics and Kibble-Zurek scaling.

## Key findings

- Universal functions for correlation and cumulant constructed
- Scaling functions are insensitive to initial temperature
- Results applicable to hot QCD near the critical point

## Abstract

In this paper, we explore the Kibble-Zurek scaling of the conserved charge, using the stachastic diffusion dynamics. After determining the characteristic scales $\tau_{kz}$ and $l_{kz}$ and properly rescaling the traditional correlation function and cumulant, we construct universal functions for both the two-point correlation function $C(y_1-y_2;\tau)$ and second-order cumulant $K(\Delta y,\tau)$ of the conserved charge in the critical regime, which are insensitive to the initial temperature and a parameter in the mapping between 3D Ising model and the hot QCD system near the critical point.