Baryon Number Dirac Spectrum in QCD

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 $\mu >m_{\pi }\mathrm{/}2$. 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.