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

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

2009-02-26

arxiv.org/abs/0902.4686v2

Physics

High Energy Physics

High Energy Physics - Lattice

20 pages, 6 eps figures, discussion on the severeness of the sign problem added, to appear in JHEP

Scientific paper

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].

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