Yang--Mills Configurations from 3D Riemann--Cartan Geometry

Recently, the {\it spacelike} part of the $SU(2)$ Yang--Mills equations has been identified with geometrical objects of a three--dimensional space of constant Riemann--Cartan curvature. We give a concise derivation of this Ashtekar type (``inverse Kaluza--Klein") {\it mapping} by employing a $(3+1)$--decomposition of {\it Clifford algebra}--valued torsion and curvature two--forms. In the subcase of a mapping to purely axial 3D torsion, the corresponding Lagrangian consists of the translational and Lorentz {\it Chern--Simons term} plus cosmological term and is therefore of purely topological origin.Comment: 14 pages, preprint Cologne-thp-1994-h1

Quantum spin Hall effect and spin-charge separation in a kagome lattice

A two-dimensional kagome lattice is theoretically investigated within a simple tight-binding model, which includes the nearest neighbor hopping term and the intrinsic spin-orbit interaction between the next nearest neighbors. By using the topological winding properties of the spin-edge states on the complex-energy Riemann surface, the spin Hall conductance is obtained to be quantized as $-e/2\pi$ ($e/2\pi$) in insulating phases. This result keeps consistent with the numerical linear-response calculation and the \textbf{Z}$_{2}$ topological invariance analysis. When the sample boundaries are connected in twist, by which two defects with $\pi$ flux are introduced, we obtain the spin-charge separated solitons at 1/3 (or 2/3) filling.Comment: 13 NJP pages, 7 figure

On the chiral anomaly in non-Riemannian spacetimes

The translational Chern-Simons type three-form coframe torsion on a Riemann-Cartan spacetime is related (by differentiation) to the Nieh-Yan four-form. Following Chandia and Zanelli, two spaces with non-trivial translational Chern-Simons forms are discussed. We then demonstrate, firstly within the classical Einstein-Cartan-Dirac theory and secondly in the quantum heat kernel approach to the Dirac operator, how the Nieh-Yan form surfaces in both contexts, in contrast to what has been assumed previously.Comment: 18 pages, RevTe

Flat-Bands on Partial Line Graphs -- Systematic Method for Generating Flat-Band Lattice Structures

We introduce a systematic method for constructing a class of lattice structures that we call ``partial line graphs''.In tight-binding models on partial line graphs, energy bands with flat energy dispersions emerge.This method can be applied to two- and three-dimensional systems. We show examples of partial line graphs of square and cubic lattices. The method is useful in providing a guideline for synthesizing materials with flat energy bands, since the tight-binding models on the partial line graphs provide us a large room for modification, maintaining the flat energy dispersions.Comment: 9 pages, 4 figure

Angularly excited and interacting boson stars and Q-balls

We study angularly excited as well as interacting non-topological solitons, so-called Q-balls and their gravitating counterparts, so-called boson stars in 3+1 dimensions. Q-balls and boson stars carry a non-vanishing Noether charge and arise as solutions of complex scalar field models in a flat space-time background and coupled minimally to gravity, respectively. We present examples of interacting Q-balls that arise due to angular excitations, which are closely related to the spherical harmonics. We also construct explicit examples of rotating boson stars that interact with non-rotating boson stars. We observe that rotating boson stars tend to absorb the non-rotating ones for increasing, but reasonably small gravitational coupling. This is a new phenomenon as compared to the flat space-time limit and is related to the negative contribution of the rotation term to the energy density of the solutions. In addition, our results indicate that a system of a rotating and non-rotating boson star can become unstable if the direct interaction term in the potential is large enough. This instability is related to the appearance of ergoregions.Comment: 20 pages including 9 figures; for higher quality figures please contact the authors; v2: minor changes, final version to appear in Phys. Rev.

Comparisons of soil physical characteristics in long-term tillage winter wheat-fallow tillage experiments

Soil physical characteristics resulting from tillage of fallow-wheat (Triticurn aestivurn L.) cropping systems were compared for two soils in western Nebraska. The soil physical environment influences the amount of water entering soil and the microenvironment that influences soil biological processes important to plant response. Effects of tillage on physical properties varied with soil type and depth of soil tillage. Generally, the 0-76 mm surface layer has the largest number of physical properties that differ as a result of tillage; however, only a few properties differed at greater depths. The Alliance silt loam (fine silty, mixed, mesic, Aridic Arguistoll) soil at the Previously Cultivated site, for example, showed differences in bulk density, hydraulic conductivity, ratio of air to water permeability, and total porosity for the 0-76 mm layer but only hydraulic conductivity was different at the 76-152 mm depth. A similar frequency of differences in physical properties was also true in the 0-76 mm layer for the Duroc loam (fine silty, mixed, mesic, Pachic Haplustoll) soil at the Native Sod site. Compared among treatments, water content, bulk density, and pore space differed in the 0-76 mm layer, while all properties different in the 76-152 mm layer, and there were fewer differences in the 152-304 mm layer in the Native Sod site. The sod treatment usually was the most extreme value with the tillage treatment values clustered together. Air to water permeability ratio, as an indicator of structural stability (ratio of 1 being stable), for the Alliance soil ranged from 18 to 43 in the 0-76 mm layer and from 31 to 152 in the 76-152 mm layer. For the Duroc soil, the ratio ranged from 5 to 6 in the 0-76 mm layer and 6 to 22 in the 76-152 mm layer. The Duroc soil has not been cropped as long as the Alliance soil and showed a tendency to be more structurally stable. Based on precipitation intensity records and infiltration characteristics, water would seldom run off the Duroc soil when in sod and with sub-till or no-till. Results show that the runoff would occur most frequently from the plow treatment

Symmetry breaking in (gravitating) scalar field models describing interacting boson stars and Q-balls

We investigate the properties of interacting Q-balls and boson stars that sit on top of each other in great detail. The model that describes these solutions is essentially a (gravitating) two-scalar field model where both scalar fields are complex. We construct interacting Q-balls or boson stars with arbitrarily small charges but finite mass. We observe that in the interacting case - where the interaction can be either due to the potential or due to gravity - two types of solutions exist for equal frequencies: one for which the two scalar fields are equal, but also one for which the two scalar fields differ. This constitutes a symmetry breaking in the model. While for Q-balls asymmetric solutions have always corresponding symmetric solutions and are thus likely unstable to decay to symmetric solutions with lower energy, there exists a parameter regime for interacting boson stars, where only asymmetric solutions exist. We present the domain of existence for two interacting non-rotating solutions as well as for solutions describing the interaction between rotating and non-rotating Q-balls and boson stars, respectively.Comment: 33 pages including 21 figures; v2: version considerably extended: 6 new figures added, equations of motion added, discussion on varying gravitational coupling added, references adde

Flat-Band Ferromagnetism in Organic Polymers Designed by a Computer Simulation

By coupling a first-principles, spin-density functional calculation with an exact diagonalization study of the Hubbard model, we have searched over various functional groups for the best case for the flat-band ferromagnetism proposed by R. Arita et al. [Phys. Rev. Lett. {\bf 88}, 127202 (2002)] in organic polymers of five-membered rings. The original proposal (poly-aminotriazole) has turned out to be the best case among the materials examined, where the reason why this is so is identified here. We have also found that the ferromagnetism, originally proposed for the half-filled flat band, is stable even when the band filling is varied away from the half-filling. All these make the ferromagnetism proposed here more experimentally inviting.Comment: 11 pages, 13figure