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, ${\hat{I}}_0^3(D+m)$, 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 $\hat{I}¼>m_{\ddot{I}}€/2$. 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