1,086 research outputs found
Anderson Localization in Quark-Gluon Plasma
At low temperature the low end of the QCD Dirac spectrum is well described by
chiral random matrix theory. In contrast, at high temperature there is no
similar statistical description of the spectrum. We show that at high
temperature the lowest part of the spectrum consists of a band of statistically
uncorrelated eigenvalues obeying essentially Poisson statistics and the
corresponding eigenvectors are extremely localized. Going up in the spectrum
the spectral density rapidly increases and the eigenvectors become more and
more delocalized. At the same time the spectral statistics gradually crosses
over to the bulk statistics expected from the corresponding random matrix
ensemble. This phenomenon is reminiscent of Anderson localization in disordered
conductors. Our findings are based on staggered Dirac spectra in quenched SU(2)
lattice simulations.Comment: 11 pages, 8 figure
Poisson to Random Matrix Transition in the QCD Dirac Spectrum
At zero temperature the lowest part of the spectrum of the QCD Dirac operator
is known to consist of delocalized modes that are described by random matrix
statistics. In the present paper we show that the nature of these eigenmodes
changes drastically when the system is driven through the finite temperature
cross-over. The lowest Dirac modes that are delocalized at low temperature
become localized on the scale of the inverse temperature. At the same time the
spectral statistics changes from random matrix to Poisson statistics. We
demonstrate this with lattice QCD simulations using 2+1 flavors of light
dynamical quarks with physical masses. Drawing an analogy with Anderson
transitions we also examine the mobility edge separating localized and
delocalized modes in the spectrum. We show that it scales in the continuum
limit and increases sharply with the temperature.Comment: 10 pages, 9 eps figures, a few references added and typos correcte
Anderson transition and multifractals in the spectrum of the Dirac operator of Quantum Chromodynamics at high temperature
We investigate the Anderson transition found in the spectrum of the Dirac
operator of Quantum Chromodynamics (QCD) at high temperature, studying the
properties of the critical quark eigenfunctions. Applying multifractal
finite-size scaling we determine the critical point and the critical exponent
of the transition, finding agreement with previous results, and with available
results for the unitary Anderson model. We estimate several multifractal
exponents, finding also in this case agreement with a recent determination for
the unitary Anderson model. Our results confirm the presence of a true Anderson
localization-delocalization transition in the spectrum of the quark Dirac
operator at high-temperature, and further support that it belongs to the 3D
unitary Anderson model class.Comment: 10 pages, 6 figure
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