Hydrodynamical Description of the QCD Dirac Spectrum at Finite Chemical Potential

TL;DR

This paper models the QCD Dirac spectrum at finite chemical potential as an incompressible droplet in the complex plane, revealing universal hydrodynamic properties and relaxation dynamics influenced by odd viscosity.

Contribution

It introduces a hydrodynamical framework for the QCD Dirac spectrum at finite chemical potential, highlighting universal ratios and collective excitation spectra.

Findings

The spectrum forms an incompressible droplet in complex eigenvalue space.

The fluctuation spectrum includes a gapped plasmon mode with odd viscosity.

Relaxation times are determined by plasmon frequencies and universal viscosity-to-density ratios.

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 $\beta=1,2,4$.