Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1998-03-23
Nucl.Phys. B525 (1998) 738-752
Physics
High Energy Physics
High Energy Physics - Phenomenology
19 pages, Latex and 8 postscript figures; explained the meaning of associated Goldstone bosons and corrected typos
Scientific paper
10.1016/S0550-3213(98)00424-6
Eigenvalues and eigenfunctions of the QCD Dirac operator are studied for gauge field configurations given by a liquid of instantons. We find that for energy differences $\delta E$ below an energy scale $E_c$ the eigenvalue correlations are given by Random Matrix Theories with the chiral symmetries of the QCD partition function. For eigenvalues near zero this energy scale shows a weak volume dependence that is not consistent with $E_c \sim 1/L^2$ which might be expected from the pion Compton wavelength and from the behavior of the Thouless energy in mesoscopic systems. However, the numerical value of $E_c$ for our largest volumes is in rough agreement with estimates from the pion Compton wavelength. A scaling behaviour consistent with $E_c\sim 1/L^2$ is found in the bulk of the spectrum. For $\delta E> E_c$ the number variance shows a linear dependence with a slope which is larger than the nonzero multifractality index of the wave functions. Finally, the average spectral density and the scalar susceptibilities are discussed in the context of quenched chiral perturbation theory. We argue that a nonzero value of the disconnected scalar susceptibility requires a linear dependence of the number variance on $\delta E$.
Osborn James C.
Verbaarschot Jacobus J. M.
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