Learning Langevin dynamics with QCD phase transition

Lingxiao Wang,Kai Zhou,Lijia Jiang,G David,Z Xu,P Garg,A Kalweit,T Ullrich,S Mukherjee,I.-K Yoo

doi:10.1051/epjconf/202225910017

Abstract

In this proceeding, the deep Convolutional Neural Networks(CNNs) are deployed to recognize the order of QCD phase transition and predict the dynamical parameters in Langevin processes. To overcome the intrinsic randomness existed in a stochastic process, we treat the final spectra as image-type inputs which preserve sufficient spatiotemporal correlations. As a practical example, we demonstrate this paradigm for the scalar condensation in QCD matter near the critical point, in which the order parameter of chiral phase transition can be characterized in a 1+1-dimensional Langevin equation for σ field. The well-trained CNNs accurately classify the first-order phase transition and crossover from σ field configurations with fluctuations, in which the noise does not impair the performance of the recognition. In reconstructing the dynamics, we demonstrate it is robust to extract the damping coefficients η from the intricate field configurations.

Highlights

Phase transition and critical phenomena are extensively observed in various many-body systems
The intrinsic randomness breaks the deterministic description of the dynamics, which hinders our further understanding to those exotic non-equilibrium systems, e.g., heavy-quark diffusion in the Quark-Gluon Plasma(QGP) [1, 2]
The Langevin dynamics is a general description of a non-equilibrium system as a stochastic differential equation, in which the degree of freedom typically are the collective variables changing very slowly, compared to the other microscopic variables in the system

Summary

Introduction

Phase transition and critical phenomena are extensively observed in various many-body systems. The model-free prediction on state evolution has been discussed with machine learning for chaotic dynamical systems [12].

Results

Conclusion