Remarks on Existence of Proper Action for Reducible Gauge Theories

In the field-antifield formalism, we review existence and uniqueness proofs for the proper action in the reducible case. We give two new existence proofs based on two resolution degrees called "reduced antifield number" and "shifted antifield number", respectively. In particular, we show that for every choice of gauge generators and their higher stage counterparts, there exists a proper action that implements them at the quadratic order in the auxiliary variables.Comment: 37 pages, LaTeX. v2,v3: Minor corrections. v4: Added reference. To appear in IJMP

Quantized Transport in Two-Dimensional Spin-Ordered Structures

We study in detail the transport properties of a model of conducting electrons in the presence of double-exchange between localized spins arranged on a 2D Kagome lattice, as introduced by Ohgushi, Murakami, and Nagaosa (2000). The relationship between the canting angle of the spin texture $\theta$ and the Berry phase field flux per triangular plaquette $\phi$ is derived explicitly and we emphasize the similarities between this model and Haldane's honeycomb lattice version of the quantum Hall effect (Haldane, 1988). The quantization of the transverse (Hall) conductivity $\sigma_{xy}$ is derived explicitly from the Kubo formula and a direct calculation of the longitudinal conductivity $\sigma_{xx}$ shows the existence of a metal-insulator transition as a function of the canting angle $\theta$ (or flux density $\phi$). This transition might be linked to that observable in the manganite compounds or in the pyrochlore ones, as the spin ordering changes from ferromagnetic to canted.Comment: 17 pages, 12 figure

Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning

We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schr\"odinger equation is mapped onto a non-linear statistical regression problem of reduced complexity. Regression models are trained on and compared to atomization energies computed with hybrid density-functional theory. Cross-validation over more than seven thousand small organic molecules yields a mean absolute error of ~10 kcal/mol. Applicability is demonstrated for the prediction of molecular atomization potential energy curves

Spin currents in rough graphene nanoribbons: Universal fluctuations and spin injection

We investigate spin conductance in zigzag graphene nanoribbons and propose a spin injection mechanism based only on graphitic nanostructures. We find that nanoribbons with atomically straight, symmetric edges show zero spin conductance, but nonzero spin Hall conductance. Only nanoribbons with asymmetrically shaped edges give rise to a finite spin conductance and can be used for spin injection into graphene. Furthermore, nanoribbons with rough edges exhibit mesoscopic spin conductance fluctuations with a universal value of $\mathrm{rms} G_\mathrm{s}\approx 0.4 e/4\pi$.Comment: 4 pages, 5 figures, PdfLaTeX, accepted for publication in Physical Review Letter

Edge effects in graphene nanostructures: II. Semiclassical theory of spectral fluctuations and quantum transport

We investigate the effect of different edge types on the statistical properties of both the energy spectrum of closed graphene billiards and the conductance of open graphene cavities in the semiclassical limit. To this end, we use the semiclassical Green's function for ballistic graphene flakes that we have derived in Reference 1. First we study the spectral two point correlation function, or more precisely its Fourier transform the spectral form factor, starting from the graphene version of Gutzwiller's trace formula for the oscillating part of the density of states. We calculate the two leading order contributions to the spectral form factor, paying particular attention to the influence of the edge characteristics of the system. Then we consider transport properties of open graphene cavities. We derive generic analytical expressions for the classical conductance, the weak localization correction, the size of the universal conductance fluctuations and the shot noise power of a ballistic graphene cavity. Again we focus on the effects of the edge structure. For both, the conductance and the spectral form factor, we find that edge induced pseudospin interference affects the results significantly. In particular intervalley coupling mediated through scattering from armchair edges is the key mechanism that governs the coherent quantum interference effects in ballistic graphene cavities