From Perturbation Theory to Confinement: How the String Tension is built up

We study the spatial volume dependence of electric flux energies for SU(2) Yang-Mills fields on the torus with twisted boundary conditions. The results approach smoothly the rotational invariant Confinement regime. The would-be string tension is very close to the infinite volume result already for volumes of $(1.2 \ {\rm fm.})^3$. We speculate on the consequences of our result for the Confinement mechanism.Comment: 6p, ps-file (uuencoded). Contribution to Lattice'93 Conference (Dallas, 1993). Preprint INLO-PUB 18/93, FTUAM-93/4

A model for conservative chaos constructed from multi-component Bose-Einstein condensates with a trap in 2 dimensions

To show a mechanism leading to the breakdown of a particle picture for the multi-component Bose-Einstein condensates(BECs) with a harmonic trap in high dimensions, we investigate the corresponding 2-$d$ nonlinear Schr{\"o}dinger equation (Gross-Pitaevskii equation) with use of a modified variational principle. A molecule of two identical Gaussian wavepackets has two degrees of freedom(DFs), the separation of center-of-masses and the wavepacket width. Without the inter-component interaction(ICI) these DFs show independent regular oscillations with the degenerate eigen-frequencies. The inclusion of ICI strongly mixes these DFs, generating a fat mode that breaks a particle picture, which however can be recovered by introducing a time-periodic ICI with zero average. In case of the molecule of three wavepackets for a three-component BEC, the increase of amplitude of ICI yields a transition from regular to chaotic oscillations in the wavepacket breathing.Comment: 5 pages, 4 figure

Isolated vacua in supersymmetric Yang-Mills theories

An explicit proof of the existence of nontrivial vacua in the pure supersymmetric Yang-Mills theories with higher orthogonal SO(N), N>=7 or the G_2 gauge group defined on a 3-torus with periodic boundary conditions is given. Extra vacuum states are separated by an energy barrier from the perturbative vacuum A_i=0 and its gauge copies.Comment: 8 pages, no figures, late