Chiral Disorder and QCD at Finite Chemical Potential

Abstract

We investigate the effects of a finite chemical potential $\mu$ in QCD viewed as a disordered medium. In the quenched approximation, $A_4=i\mu$ induces a complex electric Aharonov-Bohm effect that causes the diagonal contribution to the quark return probability to vanish at $\mu=m_{\pi}/2$ (half the pion mass). In two-color QCD, the weak-localization contribution to the quark return probability remains unaffected causing a mutation in the spectral statistics. In full QCD, the complex electric flux is screened and the light quarks are shown to diffuse asymmetrically with a substantial decrease in the conductivity along the `spatial' directions. Mean-field arguments suggest that a d=1 percolation transition may take place in the range $1.5\rho_0<\rho<3\rho_0$, where $\rho_0$ is nuclear matter density.