Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 $\Delta \tau=\pi\rho(0)/2\beta N$ with
$\rho(0)$ the spectral density at zero virtuality and $\beta=1,2,4$ for the
three Dyson ensembles that characterize QCD with different quark
representations in the ergodic regime.

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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph