Panel collapse and its applications

We describe a procedure called panel collapse for replacing a CAT(0) cube complex $\Psi$ by a "lower complexity" CAT(0) cube complex $\Psi_\bullet$ whenever $\Psi$ contains a codimension-$2$ hyperplane that is extremal in one of the codimension-$1$ hyperplanes containing it. Although $\Psi_\bullet$ is not in general a subcomplex of $\Psi$, it is a subspace consisting of a subcomplex together with some cubes that sit inside $\Psi$ "diagonally". The hyperplanes of $\Psi_\bullet$ extend to hyperplanes of $\Psi$. Applying this procedure, we prove: if a group $G$ acts cocompactly on a CAT(0) cube complex $\Psi$, then there is a CAT(0) cube complex $\Omega$ so that $G$ acts cocompactly on $\Omega$ and for each hyperplane $H$ of $\Omega$, the stabiliser in $G$ of $H$ acts on $H$ essentially. Using panel collapse, we obtain a new proof of Stallings's theorem on groups with more than one end. As another illustrative example, we show that panel collapse applies to the exotic cubulations of free groups constructed by Wise. Next, we show that the CAT(0) cube complexes constructed by Cashen-Macura can be collapsed to trees while preserving all of the necessary group actions. (It also illustrates that our result applies to actions of some non-discrete groups.) We also discuss possible applications to quasi-isometric rigidity for certain classes of graphs of free groups with cyclic edge groups. Panel collapse is also used in forthcoming work of the first-named author and Wilton to study fixed-point sets of finite subgroups of $\mathrm{Out}(F_n)$ on the free splitting complex. Finally, we apply panel collapse to a conjecture of Kropholler, obtaining a short proof under a natural extra hypothesis.Comment: Revised according to referee comments. This version accepted in "Groups, Geometry, and Dynamics

Materials review for improved automotive gas turbine engine

The potential role of superalloys, refractory alloys, and ceramics in the hottest sections of engines operating with turbine inlet temperatures as high as 1370 C is examined. The convential superalloys, directionally solidified eutectics, oxide dispersion strenghened alloys, and tungsten fiber reinforced superalloys are reviewed and compared on the basis of maximum turbine blade temperature capability. Improved high temperature protective coatings and special fabrication techniques for these advanced alloys are discussed. Chromium, columbium, molybdenum, tantalum, and tungsten alloys are also reviewed. Molbdenum alloys are found to be the most suitable for mass produced turbine wheels. Various forms and fabrication processes for silicon nitride, silicon carbide, and SIALON's are investigated for use in highstress and medium stress high temperature environments

Static quark-antiquark potential and Dirac eigenvector correlators

We represent the Polyakov loop correlator as a spectral sum of correlators of eigenvectors of the lattice Dirac operator. This spectral representation is studied numerically using quenched SU(3) configurations below and above the deconfinement temperature. We analyze whether the individual Dirac eigenvector correlators differ in the confined and deconfined phases. The decay properties of the normalized Dirac eigenvector correlators turn out to be essentially identical in the two phases, but the amplitudes change. This change of the amplitudes shifts the relative contributions of the individual Dirac eigenvector correlators and is the driving mechanism for the transition from the confining static potential into the deconfining one

New Gauge Invariant Formulation of the Chern-Simons Gauge Theory

A new gauge invariant formulation of the relativistic scalar field interacting with Chern-Simons gauge fields is considered. This formulation is consistent with the gauge fixed formulation. Furthermore we find that canonical (Noether) Poincar\'e generators are not gauge invariant even on the constraints surface and do not satisfy the (classical) Poincar\'e algebra. It is the improved generators, constructed from the symmetric energy-momentum tensor, which are (manifestly) gauge invariant and obey the classical Poincar\'e algebra.Comment: Shortened, to appear as Papid Communication-PRD/Nov/9

Supersymmetry and the Chiral Schwinger Model

We have constructed the N=1/2 supersymmetric general Abelian model with asymmetric chiral couplings. This leads to a N=1/2 supersymmetrization of the Schwinger model. We show that the supersymmetric general model is plagued with problems of infrared divergence. Only the supersymmetric chiral Schwinger model is free from such problems and is dynamically equivalent to the chiral Schwinger model because of the peculiar structure of the N=1/2 multiplets.Comment: one 9 pages Latex file, one ps file with one figur

Quantification of finite-temperature effects on adsorption geometries of π\pi-conjugated molecules

The adsorption structure of the molecular switch azobenzene on Ag(111) is investigated by a combination of normal incidence x-ray standing waves and dispersion-corrected density functional theory. The inclusion of non-local collective substrate response (screening) in the dispersion correction improves the description of dense monolayers of azobenzene, which exhibit a substantial torsion of the molecule. Nevertheless, for a quantitative agreement with experiment explicit consideration of the effect of vibrational mode anharmonicity on the adsorption geometry is crucial.Comment: 12 pages, 3 figure

Operator Ordering Problem of the Nonrelativistic Chern-Simons Theory

The operator ordering problem due to the quantization or regularization ambiguity in the Chern-Simons theory exists. However, we show that this can be avoided if we require Galilei covariance of the nonrelativistic Abelian Chern-Simons theory even at the quantum level for the extended sources. The covariance can be recovered only by choosing some particular operator orderings for the generators of the Galilei group depending on the quantization ambiguities of the $gauge-matter$ commutation relation. We show that the desired ordering for the unusual prescription is not the same as the well-known normal ordering but still satisfies all the necessary conditions. Furthermore, we show that the equations of motion can be expressed in a similar form regardless of the regularization ambiguity. This suggests that the different regularization prescriptions do not change the physics. On the other hand, for the case of point sources the regularization prescription is uniquely determined, and only the orderings, which are equivalent to the usual one, are allowed.Comment: 18 page

On the existence of Killing vector fields

In covariant metric theories of coupled gravity-matter systems the necessary and sufficient conditions ensuring the existence of a Killing vector field are investigated. It is shown that the symmetries of initial data sets are preserved by the evolution of hyperbolic systems.Comment: 9 pages, no figure, to appear in Class. Quant. Gra

Anyonic physical observables and spin phase transition

The quantization of charged matter system coupled to Chern-Simons gauge fields is analyzed in a covariant gauge fixing, and gauge invariant physical anyon operators satisfying fractional statistics are constructed in a symmetric phase, based on Dirac's recipe performed on QED. This method provides us a definite way of identifying physical spectrums free from gauge ambiguity and constructing physical anyon operators under a covariant gauge fixing. We then analyze the statistical spin phase transition in a symmetry-broken phase and show that the Higgs mechanism transmutes an anyon satisfying fractional statistics into a canonical boson, a spin 0 Higgs boson or a topologically massive photon.Comment: 14 pages, added references, a few improvement