Degenerate distributions in complex Langevin dynamics: one-dimensional QCD at finite chemical potential

2010/06/30 by Gert Aarts, K. Splittorff
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Degenerate energy levels #Dirac operator #Fermion #Flow (mathematics) #High-Energy Particle Collisions Research #Langevin dynamics #Langevin equation #Operator (biology) #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Spectrum (functional analysis) #hep-lat #hep-th #nucl-th

paper · pdf · doi:10.1007/jhep08(2010)017

published as JHEP 1008:017,2010 · 20 pages, several eps figures, minor comments added, to appear in JHEP

arxiv created 2010/07/15 · openalex publication_date 2010/08/01 · arxiv updated 2014/11/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We demonstrate analytically that complex Langevin dynamics can solve the sign problem in one-dimensional QCD in the thermodynamic limit. In particular, it is shown that the contributions from the complex and highly oscillating spectral density of the Dirac operator to the chiral condensate are taken into account correctly. We find an infinite number of classical fixed points of the Langevin flow in the thermodynamic limit. The correct solution originates from a continuum of degenerate distributions in the complexified space.

Citations

• Critical point of QCD at finite T and , lattice results for physical quark masses
• Simulating Nonequilibrium Quantum Fields with Stochastic Quantization Techniques
• Random Matrix Model of QCD at Finite Density and the Nature of the Quenched Limit
• Complex Langevin dynamics at finite chemical potential: mean field analysis in the relativistic Bose gas
• Can Stochastic Quantization Evade the Sign Problem? The Relativistic Bose Gas at Finite Chemical Potential