Baryon Number Dirac Spectrum in QCD

Abstract

The relation between the baryon number in QCD at nonzero chemical potential and the spectral density of the baryon number Dirac operator, ${\gamma }_0(D+m)$, is examined. We show that extreme oscillations of the spectral density, caused by the QCD sign problem, are essential for the formation of the average baryon number when $\mu >m_{\pi }/2$. We compute the oscillating region of the spectral density using chiral perturbation theory. The extreme oscillations have a microscopic period and are resolved using random matrix theory.

23 pages, 6 figures

References in corpus (7)

• Spectrum of the Wilson Dirac Operator at Finite Lattice Spacings
• Matrix Models and QCD with Chemical Potential
• Random matrix theory of unquenched two-colour QCD with nonzero chemical potential
• Chiral Condensate at Nonzero Chemical Potential in the Microscopic Limit of QCD
• The Wilson Dirac Spectrum for QCD with Dynamical Quarks
• QCD in One Dimension at Nonzero Chemical Potential
• Phase Diagram of the Dirac Spectrum at Nonzero Chemical Potential

Cited by in corpus (5)

• Products of Independent Gaussian Random Matrices
• The Dirac spectrum in Complex Langevin Simulations of QCD
• The QCD sign problem as a total derivative
• A subset solution to the sign problem in random matrix simulations
• Silver Blaze Puzzle in 1/Nc Expansions of Cold and Dense QCD Matter