We have studied numerically Faddeev-Hopf knots, which are defined as those unit-vector fields in R 3 that have a nontrivial Hopf charge and minimize Faddeev's Lagrangian. A given initial configuration was allowed to relax into a (local) minimum using the first order dissipative dynamics corresponding to the steepest descent method. A linked combination of two un-knots was seen to relax into different minimum energy configurations depending on their charges and their relative handedness and direction. In order to visualize the results we plot certain gaugeinvariant iso-surfaces.

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We present a combination of theoretical calculations and experiments for the low-lying vibrational excitations of H and D atoms adsorbed on the Pt(111) surface. The vibrational band states are calculated based on the full three-dimensional adiabatic potential energy surface obtained from first principles calculations. For coverages less than three quarters of a monolayer, the observed experimental high-resolution electron peaks at 31 and 68meV are in excellent agreement with the theoretical transitions between selected bands. Our results convincingly demonstrate the need to go beyond the local harmonic oscillator picture to understand the dynamics of this system.Comment: In press at Phys. Rev. Lett - to appear in April 200

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