Open AccessSpectral properties of the overlap Dirac operator in QCD
Author(s) -
Wolfgang Bietenholz,
S. Shcheredin,
Karl Jansen
Publication year - 2003
Publication title -
journal of high energy physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.998
H-Index - 261
eISSN - 1126-6708
pISSN - 1029-8479
DOI - 10.1088/1126-6708/2003/07/033
Subject(s) - dirac operator , quantum chromodynamics , random matrix , eigenvalues and eigenvectors , chiral perturbation theory , physics , conjecture , dirac (video compression format) , perturbation theory (quantum mechanics) , operator (biology) , mathematical physics , distribution (mathematics) , matrix (chemical analysis) , quantum mechanics , mathematics , mathematical analysis , pure mathematics , neutrino , gene , materials science , composite material , biochemistry , chemistry , repressor , transcription factor
We discuss the eigenvalue distribution of the overlap Dirac operator inquenched QCD on lattices of size 8^{4}, 10^{4} and 12^{4} at \beta = 5.85 and\beta = 6. We distinguish the topological sectors and study the distributionsof the leading non-zero eigenvalues, which are stereographically mapped ontothe imaginary axis. Thus they can be compared to the predictions of randommatrix theory applied to the \epsilon-expansion of chiral perturbation theory.We find a satisfactory agreement, if the physical volume exceeds about (1.2fm)^{4}. For the unfolded level spacing distribution we find an accurateagreement with the random matrix conjecture on all volumes that we considered.Comment: 16 pages, 8 figures, final version published in JHE
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