191 research outputs found
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
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
Evidence for quantum chaos in the plasma phase of QCD
We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3)
gauge theory and in full QCD on a lattice. As a measure of the
fluctuation properties of the eigenvalues, we study the nearest-neighbor
spacing distribution for various values of both in the
confinement and in the deconfinement phase. In both phases except far into the
deconfinement region, the lattice data agree with the Wigner surmise of
random-matrix theory which is indicative of quantum chaos. We do not find signs
of a transition to Poisson regularity at the deconfinement phase transition.Comment: 8 pages, 10 figures (included), acknowledgement complete
Random Matrix Theory, Chiral Perturbation Theory, and Lattice Data
Recently, the chiral logarithms predicted by quenched chiral perturbation
theory have been extracted from lattice calculations of hadron masses. We argue
that the deviations of lattice results from random matrix theory starting
around the so-called Thouless energy can be understood in terms of chiral
perturbation theory as well. Comparison of lattice data with chiral
perturbation theory formulae allows us to compute the pion decay constant. We
present results from a calculation for quenched SU(2) with Kogut-Susskind
fermions at \beta=2.0 and 2.2.Comment: LaTeX, 12 pages, 7 .eps figure
Random Matrix Theory and Chiral Logarithms
Recently, the contributions of chiral logarithms predicted by quenched chiral
perturbation theory have been extracted from lattice calculations of hadron
masses. We argue that a detailed comparison of random matrix theory and lattice
calculations allows for a precise determination of such corrections. We
estimate the relative size of the m*log(m), m, and m^2 corrections to the
chiral condensate for quenched SU(2).Comment: LaTeX (elsart.cls), 9 pages, 6 .eps figures, added reference, altered
discussion of Eq.(9
Beyond the Thouless energy
The distribution and the correlations of the small eigenvalues of the Dirac
operator are described by random matrix theory (RMT) up to the Thouless energy
, where is the physical volume. For somewhat larger
energies, the same quantities can be described by chiral perturbation theory
(chPT). For most quantities there is an intermediate energy regime, roughly
, where the results of RMT and chPT agree with each other. We
test these predictions by constructing the connected and disconnected scalar
susceptibilities from Dirac spectra obtained in quenched SU(2) and SU(3)
simulations with staggered fermions for a variety of lattice sizes and coupling
constants. In deriving the predictions of chPT, it is important to take into
account only those symmetries which are exactly realized on the lattice.Comment: LATTICE99(Theoretical Developments), 3 pages, 3 figures, typo in Ref.
[10] correcte
Report drawn up on behalf of the Committee on Budgetary Control on the budgetary costs of the common agricultural policy in the cereals sector and the factors which may influence these costs. Working Documents 1982-1983, Document 1-680/82, 15 October 1982
- …