Anomalous Diffusion in Infinite Horizon Billiards

We consider the long time dependence for the moments of displacement < |r|^q > of infinite horizon billiards, given a bounded initial distribution of particles. For a variety of billiard models we find ~ t^g(q) (up to factors of log t). The time exponent, g(q), is piecewise linear and equal to q/2 for q2. We discuss the lack of dependence of this result on the initial distribution of particles and resolve apparent discrepancies between this time dependence and a prior result. The lack of dependence on initial distribution follows from a remarkable scaling result that we obtain for the time evolution of the distribution function of the angle of a particle's velocity vector.Comment: 11 pages, 7 figures Submitted to Physical Review

Effective Potentials in QCD and Chiral Symmetry Breaking

We consider chiral symmetry breaking through nontrivial vacuum structure with an explicit construct for the vacuum with quark antiquark condensates in QCD with Coulomb gauge for different phenomenological potentials. The dimensional parameter for the condensate function gets related to $$ of Shifman, Vainshtein and Zakharov. We then relate the condensate function to the wave function of pion as a Goldstone mode. This simultaneously yields the pion also as a quark antiquark bound state as a localised zero mode of vacuum. We then calculate different pionic properties using the wave function as obtained from the vacuum structure. (to appear in Z. Phys. C)Comment: 22 pages,10 figures, IP/BBSR/92-5