Hydrodynamical Description of the QCD Dirac Spectrum at Finite Chemical Potential

Abstract

We present a hydrodynamical description of the QCD Dirac spectrum at finite chemical potential as an uncompressible droplet in the complex eigenvalue space. For a large droplet, the fluctuation spectrum around the hydrostatic solution is gapped by a longitudinal Coulomb plasmon, and exhibits a frictionless odd viscosity. The stochastic relaxation time for the restoration/breaking of chiral symmetry is set by twice the plasmon frequency. The leading droplet size correction to the relaxation time is fixed by a universal odd viscosity to density ratio $\eta_O/\rho_0=(\beta-2)/4$ for the three Dyson ensembles $\beta=1,2,4$.