Complex Langevin dynamics at finite chemical potential: mean field analysis in the relativistic Bose gas

TL;DR

This paper analytically investigates complex Langevin dynamics for the relativistic Bose gas at finite chemical potential using mean field approximation, addressing convergence, stability, and the sign problem, and compares results with numerical data.

Contribution

It provides an analytical mean field analysis of complex Langevin dynamics in the relativistic Bose gas at finite chemical potential, including stability and sign problem insights.

Findings

Mean field approximation captures key features of complex Langevin dynamics.

Constructed the real distribution satisfying the extended Fokker-Planck equation.

Compared analytical results with numerical data, showing consistency.

Abstract

Stochastic quantization can potentially be used to simulate theories with a complex action due to a nonzero chemical potential. We study complex Langevin dynamics in the relativistic Bose gas analytically, using a mean field approximation. We concentrate on the region with a Silver Blaze problem and discuss convergence, stability, fixed points, and the severeness of the sign problem. The real distribution satisfying the extended Fokker-Planck equation is constructed and its nonlocal form is explained. Finally, we compare the mean field results in finite volume with the numerical data presented in Ref. [1].