ar X iv : c on d - m at / 0 11 14 76 v 1 2 5 N ov 2 00 1 Bushes of normal modes - new dynamical objects in nonlinear mechanical systems with discrete symmetry

ar X iv : n lin / 0 51 10 57 v 1 [ nl in . C D ] 2 6 N ov 2 00 5 DISCRETE DYNAMICAL SYSTEMS EMBEDDED IN CANTOR SETS

While the notion of chaos is well established for dynamical systems on manifolds, it is not so for dynamical systems over discrete spaces with N variables, as binary neural networks and cellular automata. The main difficulty is the choice of a suitable topology to study the limit N → ∞. By embedding the discrete phase space into a Cantor set we provided a natural setting to define topological e...

ar X iv : h ep - l at / 0 11 00 06 v 3 6 N ov 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

ar X iv : h ep - t h / 05 11 19 0 v 1 1 8 N ov 2 00 5 The Dirac equation in Taub - NUT space

Using chiral supersymmetry, we show that the massless Dirac equation in the Taub-NUT gravita-tional instanton field is exactly soluble and explain the arisal and the use of the dynamical (super) symmetry. 1. Introduction The Dirac equation D ψ = 0 in the Kaluza-Klein (KK) monopole field — obtained by imbedding the Taub-NUT solution into five-dimensional gravity with trivial time dependence [1] ...

ar X iv : c on d - m at / 0 11 14 69 v 1 2 4 N ov 2 00 1 REMARKS ON THE NONLINEAR SCHRÖDINGER EQUATION WITH HARMONIC POTENTIAL

We solve the local Cauchy problem for the nonlinear Schrödinger equation with harmonic potential, an equation appearing in the study of Bose-Einstein condensation. We prove that the mathematical study of this equation is very close to the study of the same equation without potential, thanks to two explicit operators. We prove the analogue of the pseudo-conformal conservation law, and results fo...

ar X iv : h ep - l at / 0 11 10 55 v 1 2 8 N ov 2 00 1

We use low lying eigenvectors of the overlap-Dirac operator as a probe of the QCD vacuum. If instantons play a significant role one would expect the low lying eigenmodes of the overlap-Dirac operator to consist mainly of the mixed “would be zero modes”. Then, the eigenmodes should exhibit local chirality. Studying a recently introduced local chirality parameter, we find evidence supporting this...