arXiv subjects

Piotr Warchol

Publications and source records attributed to Piotr Warchol.

3 recordsLinked to original sources

arXiv2015

Hydrodynamical Description of the QCD Dirac Spectrum at Finite Chemical Potential

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 $η_O/ρ_0=(β-2)/4$ for the three Dyson ensembles $β=1,2,4$.

hep-ph↗

arXiv2015

Hydrodynamics of the Chiral Dirac Spectrum

We derive a hydrodynamical description of the eigenvalues of the chiral Dirac spectrum in the vacuum and in the large $N$ (volume) limit. The linearized hydrodynamics supports sound waves. The stochastic relaxation of the eigenvalues is captured by a hydrodynamical instanton configuration which follows from a pertinent form of Euler equation. The relaxation from a phase of localized eigenvalues and unbroken chiral symmetry to a phase of de-localized eigenvalues and broken chiral symmetry occurs over a time set by the speed of sound. We show that the time is $Δτ=πρ(0)/2βN$ with $ρ(0)$ the spectral density at zero virtuality and $β=1,2,4$ for the three Dyson ensembles that characterize QCD with different quark representations in the ergodic regime.

hep-ph↗

arXiv2015

Hydrodynamics of the Polyakov Line in SU$(N_c)$ Yang-Mills

We discuss a hydrodynamical description of the eigenvalues of the Polyakov line at large but finite $N_c$ for Yang-Mills theory in even and odd space-time dimensions. The hydro-static solutions for the eigenvalue densities are shown to interpolate between a uniform distribution in the confined phase and a localized distribution in the de-confined phase. The resulting critical temperatures are in overall agreement with those measured on the lattice over a broad range of $N_c$, and are consistent with the string model results at $N_c=\infty$. The stochastic relaxation of the eigenvalues of the Polyakov line out of equilibrium is captured by a hydrodynamical instanton. An estimate of the probability of formation of a Z(N$_c)$ bubble using a piece-wise sound wave is suggested.

hep-ph↗