55 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
Dirac eigenmodes at the QCD Anderson transition
Recently we found an Anderson-type localization-delocalization transition in
the QCD Dirac spectrum at high temperature. Using spectral statistics we
obtained a critical exponent compatible with that of the corresponding Anderson
model. Here we study the spatial structure of the eigenmodes both in the
localized and the transition region. Based on previous studies in the Anderson
model, at the critical point, the eigenmodes are expected to have a scale
invariant multifractal structure. We verify the scale invariance of Dirac
eigenmodes at the critical point.Comment: to appear in Proceedings of The 32nd International Symposium on
Lattice Field Theory, 23-28 June, 2014, Columbia University New York, N
- …