ar X iv : m at h - ph / 9 90 80 30 v 1 3 1 A ug 1 99 9 Nonlinear Hodge maps

ar X iv : m at h - ph / 9 90 80 30 v 2 2 1 O ct 1 99 9 Nonlinear Hodge maps

We consider maps between Riemannian manifolds in which the map is a stationary point of the nonlinear Hodge energy. The variational equations of this functional form a quasilinear, nondiagonal, nonuniformly elliptic system which models certain kinds of compressible flow. Conditions are found under which singular sets of prescribed dimension cannot occur. Continuity results are given for the tra...

ar X iv : c on d - m at / 9 70 80 30 v 1 [ co nd - m at . s up r - co n ] 5 A ug 1 99 7 1

ar X iv : h ep - l at / 9 90 80 26 v 1 1 9 A ug 1 99 9 1

We introduce quantum gauge fixing (QGF) as a new class of gauge fixings. While the maximal center gauge might not show vortex dominance, the confining properties of the vortices observed in past lattice calculations are argued to have been obtained in a gauge more akin to QGF than to the strict maximal center gauge.

ar X iv : h ep - l at / 9 90 80 47 v 1 2 7 A ug 1 99 9 1 Monte Carlo Hamiltonian

We suggest how to construct an effective low energy Hamiltonian via Monte Carlo starting from a given action. We test it by computing thermodynamical observables like average energy and specific heat for simple quantum systems.

ar X iv : m at h - ph / 9 90 80 09 v 1 6 A ug 1 99 9 Schrödinger Equation with Moving Point Interactions in Three Dimensions

We consider the motion of a non relativistic quantum particle in R 3 subject to n point interactions which are moving on given smooth trajec-tories. Due to the singular character of the time-dependent interaction, the corresponding Schrödinger equation does not have solutions in a strong sense and, moreover, standard perturbation techniques cannot be used. Here we prove that, for smooth initial...