General U(N) gauge transformations in the realm of covariant Hamiltonian field theory

A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. While the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, the covariant canonical transformation theory offers more general means for defining mappings that preserve the action functional - and hence the form of the field equations - than the usual Lagrangian description. Similar to the well-known canonical transformation theory of point dynamics, the canonical transformation rules for fields are derived from generating functions. As an interesting example, we work out the generating function of type F_2 of a general local U(N) gauge transformation and thus derive the most general form of a Hamiltonian density that is form-invariant under local U(N) gauge transformations.Comment: 36 pages, Symposium on Exciting Physics: Quarks and gluons/atomic nuclei/biological systems/networks, Makutsi Safari Farm, South Africa, 13-20 November 2011; Exciting Interdisciplinary Physics, Walter Greiner, Ed., FIAS Interdisciplinary Science Series, Springer International Publishing Switzerland, 201

Non-spiky density of states of an icosahedral quasicrystal

The density of states of the ideal three-dimensional Penrose tiling, a quasicrystalline model, is calculated with a resolution of 10 meV. It is not spiky. This falsifies theoretical predictions so far, that spikes of width 10-20 meV are generic for the density of states of quasicrystals, and it confirms recent experimental findings. The qualitative difference between our results and previous calculations is partly explained by the small number of k points that has usually been included in the evaluation of the density of states of periodic approximants of quasicrystals. It is also shown that both the density of states of a small approximant of the three-dimensional Penrose tiling and the density of states of the ideal two-dimensional Penrose tiling do have spiky features, which also partly explains earlier predictions.Comment: 8 pages, 4 figures. Changes in this version: longer introduction, details of figures shown in inset

Hydrogen bonding structure of confined water templated by a metal-organic framework with open metal sites.

Water in confinement exhibits properties significantly different from bulk water due to frustration in the hydrogen-bond network induced by interactions with the substrate. Here, we combine infrared spectroscopy and many-body molecular dynamics simulations to probe the structure and dynamics of confined water as a function of relative humidity within a metal-organic framework containing cylindrical pores lined with ordered cobalt open coordination sites. Building upon the agreement between experimental and theoretical spectra, we demonstrate that water at low relative humidity binds initially to open metal sites and subsequently forms disconnected one-dimensional chains of hydrogen-bonded water molecules bridging between cobalt atoms. With increasing relative humidity, these water chains nucleate pore filling, and water molecules occupy the entire pore interior before the relative humidity reaches 30%. Systematic analysis of rotational and translational dynamics indicates heterogeneity in this pore-confined water, with water molecules displaying variable mobility as a function of distance from the interface