ABSTRACT
We show that integrable structure of chiral random matrix models incorporating global symmetries of QCD Dirac operators (labeled by the Dyson index beta = 1,2, and 4) leads to emergence of a connection relation between the spectral statistics of massive and massless Dirac operators. This novel link established for beta-fold degenerate massive fermions is used to explicitly derive (and prove the random matrix universality of) statistics of low-lying spectra of QCD Dirac operators in the presence of SU(2) massive fermions in the fundamental representation ( beta = 1) and SU(N(c)>/=2) massive adjoint fermions ( beta = 4). Comparison with available lattice data for SU(2) dynamical staggered fermions reveals a good agreement.
ABSTRACT
The scattering of light from a slightly rough surface overlying a reflecting surface is investigated. It is shown that the long-scale component of the roughness spectrum plays a critical role in the scattering patterns obtained. The scattered interference patterns are critically dependent on small variation of the rms height of the long-scale component of the roughness. Conventional perturbation theory is found to be invalid in cases in which interference phenomena in the scattering are of importance. A model is proposed that quantitatively describes the measured angular intensity distributions.
