655 research outputs found
Universal correlations in spectra of the lattice QCD Dirac operator
Recently, Kalkreuter obtained complete Dirac spectra for lattice
gauge theory both for staggered fermions and for Wilson fermions. The lattice
size was as large as . We performed a statistical analysis of these data
and found that the eigenvalue correlations can be described by the Gaussian
Symplectic Ensemble for staggered fermions and by the Gaussian Orthogonal
Ensemble for Wilson fermions. In both cases long range spectral fluctuations
are strongly suppressed: the variance of a sequence of levels containing
eigenvalues on average is given by
( is equal to 4 and 1, respectively) instead of for a
random sequence of levels. Our findings are in agreement with the anti-unitary
symmetry of the lattice Dirac operator for with staggered fermions
which differs from Wilson fermions (with the continuum anti-unitary symmetry).
For , we predict that the eigenvalue correlations are given by the
Gaussian Unitary Ensemble.Comment: Talk present at LATTICE96(chirality in QCD), 3 pages, Late
Quantum chaos in QCD at finite temperature
We study complete eigenvalue spectra of the staggered Dirac matrix in
quenched QCD on a lattice. In particular, we investigate the
nearest-neighbor spacing distribution for various values of both
in the confinement and deconfinement phase. In both phases except far into the
deconfinement region, the data agree with the Wigner surmise of random matrix
theory which is indicative of quantum chaos. No signs of a transition to
Poisson regularity are found, and the reasons for this result are discussed.Comment: 3 pages, 6 figures (included), poster presented by R. Pullirsch at
"Lattice 97", to appear in the proceeding
Equivalent of a Thouless energy in lattice QCD Dirac spectra
Random matrix theory (RMT) is a powerful statistical tool to model spectral
fluctuations. In addition, RMT provides efficient means to separate different
scales in spectra. Recently RMT has found application in quantum chromodynamics
(QCD). In mesoscopic physics, the Thouless energy sets the universal scale for
which RMT applies. We try to identify the equivalent of a Thouless energy in
complete spectra of the QCD Dirac operator with staggered fermions and
lattice gauge fields. Comparing lattice data with RMT predictions we
find deviations which allow us to give an estimate for this scale.Comment: LATTICE99 (theor. devel.), 3 pages, 4 figure
Quantum chaos and QCD at finite chemical potential
We investigate the distribution of the spacings of adjacent eigenvalues of
the lattice Dirac operator. At zero chemical potential , the
nearest-neighbor spacing distribution follows the Wigner surmise of
random matrix theory both in the confinement and in the deconfinement phase.
This is indicative of quantum chaos. At nonzero chemical potential, the
eigenvalues of the Dirac operator become complex. We discuss how can be
defined in the complex plane. Numerical results from an SU(3) simulation with
staggered fermions are compared with predictions from non-hermitian random
matrix theory, and agreement with the Ginibre ensemble is found for .Comment: LATTICE98(hightemp), 3 pages, 10 figure
Comment on Dirac spectral sum rules for QCD_3
Recently Magnea hep-th/9907096 , hep-th/9912207 [Phys.Rev.D61, 056005 (2000);
Phys.Rev.D62, 016005 (2000)] claimed to have computed the first sum rules for
Dirac operators in 3D gauge theories from 0D non-linear sigma models. I point
out that these computations are incorrect, and that they contradict with the
exact results for the spectral densities unambiguously derived from random
matrix theory by Nagao and myself.Comment: REVTeX 3.1, 2 pages, no figure. (v2) redundant part removed,
conclusion unchange
Ratios of characteristic polynomials in complex matrix models
We compute correlation functions of inverse powers and ratios of characteristic polynomials for random matrix models with complex eigenvalues. Compact expressions are given in terms of orthogonal polynomials in the complex plane as well as their Cauchy transforms, generalizing previous expressions for real eigenvalues. We restrict ourselves to ratios of characteristic polynomials over their complex conjugate
Quantum Chaos in Compact Lattice QED
Complete eigenvalue spectra of the staggered Dirac operator in quenched
compact QED are studied on and lattices. We
investigate the behavior of the nearest-neighbor spacing distribution as
a measure of the fluctuation properties of the eigenvalues in the strong
coupling and the Coulomb phase. In both phases we find agreement with the
Wigner surmise of the unitary ensemble of random-matrix theory indicating
quantum chaos. Combining this with previous results on QCD, we conjecture that
quite generally the non-linear couplings of quantum field theories lead to a
chaotic behavior of the eigenvalues of the Dirac operator.Comment: 11 pages, 4 figure
Statistical analysis and the equivalent of a Thouless energy in lattice QCD Dirac spectra
Random Matrix Theory (RMT) is a powerful statistical tool to model spectral
fluctuations. This approach has also found fruitful application in Quantum
Chromodynamics (QCD). Importantly, RMT provides very efficient means to
separate different scales in the spectral fluctuations. We try to identify the
equivalent of a Thouless energy in complete spectra of the QCD Dirac operator
for staggered fermions from SU(2) lattice gauge theory for different lattice
size and gauge couplings. In disordered systems, the Thouless energy sets the
universal scale for which RMT applies. This relates to recent theoretical
studies which suggest a strong analogy between QCD and disordered systems. The
wealth of data allows us to analyze several statistical measures in the bulk of
the spectrum with high quality. We find deviations which allows us to give an
estimate for this universal scale. Other deviations than these are seen whose
possible origin is discussed. Moreover, we work out higher order correlators as
well, in particular three--point correlation functions.Comment: 24 pages, 24 figures, all included except one figure, missing eps
file available at http://pluto.mpi-hd.mpg.de/~wilke/diff3.eps.gz, revised
version, to appear in PRD, minor modifications and corrected typos, Fig.4
revise
Finding the Pion in the Chiral Random Matrix Vacuum
The existence of a Goldstone boson is demonstrated in chiral random matrix
theory. After determining the effective coupling and calculating the scalar and
pseudoscalar propagators, a random phase approximation summation reveals the
massless pion and massive sigma modes expected whenever chiral symmetry is
spontaneously broken.Comment: 3 pages, 1 figure, revte
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