Green's Functions from Quantum Cluster Algorithms

We show that cluster algorithms for quantum models have a meaning independent of the basis chosen to construct them. Using this idea, we propose a new method for measuring with little effort a whole class of Green's functions, once a cluster algorithm for the partition function has been constructed. To explain the idea, we consider the quantum XY model and compute its two point Green's function in various ways, showing that all of them are equivalent. We also provide numerical evidence confirming the analytic arguments. Similar techniques are applicable to other models. In particular, in the recently constructed quantum link models, the new technique allows us to construct improved estimators for Wilson loops and may lead to a very precise determination of the glueball spectrum.Comment: 15 pages, LaTeX, with four figures. Added preprint numbe

Alkali oxide-tantalum oxide and alkali oxide-niobium oxide ionic conductors

A search was made for new cationic conducting phases in alkali-tantalate and niobate systems. The phase equilibrium diagrams were constructed for the six binary systems Nb2O5-LiNbO3, Nb2O5-NaNbO3, Nb2O5-KNbO3, Ta2O5-NaTaO3, Ta2O5-LiTaO3, and Ta2O5-KTaO3. Various other binary and ternary systems were also examined. Pellets of nineteen phases were evaluated (by the sponsoring agency) by dielectric loss measurements. Attempts were made to grow large crystals of eight different phases. The system Ta2O5-KTaO3 contains at least three phases which showed peaks in dielectric loss vs. temperature. All three contain structures related to the tungsten bronzes with alkali ions in non-stoichiometric crystallographic positions

Alkali oxide-tantalum, niobium and antimony oxide ionic conductors

The phase equilibrium relations of four systems were investigated in detail. These consisted of sodium and potassium antimonates with antimony oxide and tantalum and niobium oxide with rubidium oxide as far as the ratio 4Rb2O:llB2O5 (B=Nb, Ta). The ternary system NaSbO3-Sb2O4-NaF was investigated extensively to determine the actual composition of the body centered cubic sodium antimonate. Various other binary and ternary oxide systems involving alkali oxides were examined in lesser detail. The phases synthesized were screened by ion exchange methods to determine mobility of the mobility of the alkali ion within the niobium, tantalum or antimony oxide (fluoride) structural framework. Five structure types warranted further investigation; these structure types are (1) hexagonal tungsten bronze (HTB), (2) pyrochlore, (3) the hybrid HTB-pyrochlore hexagonal ordered phases, (4) body centered cubic antimonates and (5) 2K2O:3Nb2O5. Although all of these phases exhibit good ion exchange properties only the pyrochlore was prepared with Na(+) ions as an equilibrium phase and as a low porosity ceramic. Sb(+3) in the channel interferes with ionic conductivity in this case, although relatively good ionic conductivity was found for the metastable Na(+) ion exchanged analogs of RbTa2O5F and KTaWO6 pyrochlore phases

Effective Lagrangian for strongly coupled domain wall fermions

We derive the effective Lagrangian for mesons in lattice gauge theory with domain-wall fermions in the strong-coupling and large-N_c limits. We use the formalism of supergroups to deal with the Pauli-Villars fields, needed to regulate the contributions of the heavy fermions. We calculate the spectrum of pseudo-Goldstone bosons and show that domain wall fermions are doubled and massive in this regime. Since we take the extent and lattice spacing of the fifth dimension to infinity and zero respectively, our conclusions apply also to overlap fermions.Comment: 26 pp. RevTeX and 3 figures; corrected error in symmetry breaking scheme and added comments to discussio

The Perfect Quark-Gluon Vertex Function

We evaluate a perfect quark-gluon vertex function for QCD in coordinate space and truncate it to a short range. We present preliminary results for the charmonium spectrum using this quasi-perfect action.Comment: 3 pages LaTex, 4 figures, poster presented at LATTICE9

Adaptive multigrid algorithm for the lattice Wilson-Dirac operator

We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix together with a simplified form of the correction based on the so-called gamma_5-Hermitian symmetry of the Dirac operator. We demonstrate that the algorithm nearly eliminates critical slowing down in the chiral limit and that it has weak dependence on the lattice volume

The Dynamics of a Meandering River

We present a statistical model of a meandering river on an alluvial plane which is motivated by the physical non-linear dynamics of the river channel migration and by describing heterogeneity of the terrain by noise. We study the dynamics analytically and numerically. The motion of the river channel is unstable and we show that by inclusion of the formation of ox-bow lakes, the system may be stabilised. We then calculate the steady state and show that it is in agreement with simulations and measurements of field data.Comment: Revtex, 12 pages, 2 postscript figure