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

TY - JOUR

T1 - Degenerate distributions in complex Langevin dynamics

T2 - one-dimensional QCD at finite chemical potential

AU - Aarts, Gert

AU - Splittorff, Kim

PY - 2010/8/3

Y1 - 2010/8/3

N2 - 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.

AB - 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.

U2 - 10.1007/jhep08(2010)017

DO - 10.1007/jhep08(2010)017

M3 - Journal article

SN - 1126-6708

VL - 2010

SP - 017

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

IS - 8

ER -