The QCD vacuum as a disordered medium: A simplified model for the QCD Dirac operator

We model the QCD Dirac operator as a power-law random banded matrix (RBM) with the appropriate chiral symmetry. Our motivation is the form of the Dirac operator in a basis of instantonic zero modes with a corresponding gauge background of instantons. We compare the spectral correlations of this model to those of an instanton liquid model (ILM) and find agreement well beyond the Thouless energy. In the bulk of the spectrum the (dimensionless) Thouless energy of the RBM scales with the square root of system size in agreement with the ILM and chiral perturbation theory. Near the origin the scaling of the (dimensionless) Thouless energy in the RBM remains the same as in the bulk which agrees with chiral perturbation theory but not with the ILM. Finally we discuss how this RBM should be modified in order to describe the spectral correlations of the QCD Dirac operator at the finite temperature chiral restoration transition.Comment: 4 pages, 3 figure

Neutrino Masses and Mixing: Where We Stand and Where We are Going

In this talk I review our present knowledge on neutrino masses and mixing as well as the expectations from near future experiments.Comment: 19 Pages, 11 figures. Review talk given at the 10th International Conference on Supersymmetry and Unification of Fundamental Interactions, SUSY02 (June 17-23, 2002, DESY, Hamburg

Reduction of Almost Poisson brackets and Hamiltonization of the Chaplygin Sphere

We construct different almost Poisson brackets for nonholonomic systems than those existing in the literature and study their reduction. Such brackets are built by considering non-canonical two-forms on the cotangent bundle of configuration space and then carrying out a projection onto the constraint space that encodes the Lagrange-D'Alembert principle. We justify the need for this type of brackets by working out the reduction of the celebrated Chaplygin sphere rolling problem. Our construction provides a geometric explanation of the Hamiltonization of the problem given by A. V. Borisov and I. S. Mamaev

[Review of] John E. Farley. Majority-Minority Relations

John E. Farley, who is on the faculty of Southern Illinois University (Edwardsville), says that he has written this book because he is concerned about the deteriorating status of minorities and intergroup relations in the United States. His main objective is to increase awareness of these issues among college students in race relations classes by not only describing but also analyzing and attempting to explain the problems which our society faces