SLˉ(4,R)\bar{SL}(4,R) Embedding for a 3D World Spinor Equation

A generic-curved spacetime Dirac-like equation in 3D is constructed. It has, owing to the $\bar{SL}(n,R)$ group deunitarizing automorphism, a physically correct unitarity and flat spacetime particle properties. The construction is achieved by embedding $\bar{SL}(3,R)$ vector operator $X_{\mu}$, that plays a role of Dirac's $\gamma_{\mu}$ matrices, into $\bar{SL}(4,R)$. Decomposition of the unitary irreducible spinorial $\bar{SL}(4,R)$ representations gives rise to an explicit form of the infinite $X_{\mu}$ matrices

Enhancement and suppression of tunneling by controlling symmetries of a potential barrier

We present a class of 2D systems which shows a counterintuitive property that contradicts a semi classical intuition: A 2D quantum particle "prefers" tunneling through a barrier rather than traveling above it. Viewing the one particle 2D system as the system of two 1D particles, it is demonstrated that this effect occurs due to a specific symmetry of the barrier that forces excitations of the interparticle degree of freedom that, in turn, leads to the appearance of an effective potential barrier even though there is no "real" barrier. This phenomenon cannot exist in 1D.Comment: 10 pages and 7 figure

Controlling the topological sector of magnetic solitons in exfoliated Cr1/3_{1/3}NbS2_2 crystals

We investigate manifestations of topological order in monoaxial helimagnet Cr$_{1/3}$NbS$_2$ by performing transport measurements on ultra-thin crystals. Upon sweeping the magnetic field perpendicularly to the helical axis, crystals thicker than one helix pitch (48 nm) but much thinner than the magnetic domain size ($\sim$1 $\mu$m) are found to exhibit sharp and hysteretic resistance jumps. We show that these phenomena originate from transitions between topological sectors with different number of magnetic solitons. This is confirmed by measurements on crystals thinner than 48 nm --in which the topological sector cannot change-- that do not exhibit any jump or hysteresis. Our results show the ability to deterministically control the topological sector of finite-size Cr$_{1/3}$NbS$_2$ and to detect inter-sector transitions by transport measurements.Comment: 7 pages, 8 figure

Zero Temperature Chiral Phase Transition in (2+1)-Dimensional QED with a Chern-Simons Term

We investigate the zero temperature chiral phase transition in (2+1)-dimensional QED in the presence of a Chern-Simons term, changing the number of fermion flavors. In the symmetric phase, there are no light degrees of freedom even at the critical point. Unlike the case without a Chern-Simons term, the phase transition is first-order.Comment: 7 pages, RevTeX, no figure

Multi-view Brain Network Prediction from a Source View Using Sample Selection via CCA-Based Multi-kernel Connectomic Manifold Learning

Several challenges emerged from the dataclysm of neuroimaging datasets spanning both healthy and disordered brain spectrum. In particular, samples with missing data views (e.g., functional imaging modality) constitute a hurdle to conventional big data learning techniques which ideally would be trained using a maximum number of samples across all views. Existing works on predicting target data views from a source data view mainly used brain images such as predicting PET image from MRI image. However, to the best of our knowledge, predicting a set of target brain networks from a source network remains unexplored. To ll this gap, a multi-kernel manifold learning (MKML) framework is proposed to learn how to predict multi-view brain networks from a source network to impute missing views in a connectomic dataset. Prior to performing multiple kernel learning of multi-view data, it is typically assumed that the source and target data come from the same distribution. However, multi-view connectomic data can be drawn from different distributions. In order to build robust predictors for predicting target multi-view networks from a source network view, it is necessary to take into account the shift between the source and target domains. Hence, we first estimate a mapping function that transforms the source and the target domains into a shared space where their correlation is maximized using canonical correlation analysis (CCA). Next, we nest the projected training and testing source samples into a connectomic manifold using multiple kernel learning, where we identify the most similar training samples to the testing source network. Given a testing subject, we introduce a cross-domain trust score to assess the reliability of each selected training sample for the target prediction task. Our model outperformed both conventional MKML technique and the proposed CCA-based MKMLtechnique without enhancement by trust scores

Observation of the Fractional Quantum Hall Effect in Graphene

When electrons are confined in two dimensions and subjected to strong magnetic fields, the Coulomb interactions between them become dominant and can lead to novel states of matter such as fractional quantum Hall liquids. In these liquids electrons linked to magnetic flux quanta form complex composite quasipartices, which are manifested in the quantization of the Hall conductivity as rational fractions of the conductance quantum. The recent experimental discovery of an anomalous integer quantum Hall effect in graphene has opened up a new avenue in the study of correlated 2D electronic systems, in which the interacting electron wavefunctions are those of massless chiral fermions. However, due to the prevailing disorder, graphene has thus far exhibited only weak signatures of correlated electron phenomena, despite concerted experimental efforts and intense theoretical interest. Here, we report the observation of the fractional quantum Hall effect in ultraclean suspended graphene, supporting the existence of strongly correlated electron states in the presence of a magnetic field. In addition, at low carrier density graphene becomes an insulator with an energy gap tunable by magnetic field. These newly discovered quantum states offer the opportunity to study a new state of matter of strongly correlated Dirac fermions in the presence of large magnetic fields

Development of biomimetic catalytic oxidation methods and non-salt methods using transition metal-based acid and base ambiphilic catalysts

This review focuses on the development of ruthenium and flavin catalysts for environmentally benign oxidation reactions based on mimicking the functions of cytochrome P-450 and flavoenzymes, and low valent transition-metal catalysts that replace conventional acids and bases. Several new concepts and new types of catalytic reactions based on these concepts are described

A Review of Target Mass Corrections

With recent advances in the precision of inclusive lepton--nuclear scattering experiments, it has become apparent that comparable improvements are needed in the accuracy of the theoretical analysis tools. In particular, when extracting parton distribution functions in the large-x region, it is crucial to correct the data for effects associated with the nonzero mass of the target. We present here a comprehensive review of these target mass corrections (TMC) to structure functions data, summarizing the relevant formulas for TMCs in electromagnetic and weak processes. We include a full analysis of both hadronic and partonic masses, and trace how these effects appear in the operator product expansion and the factorized parton model formalism, as well as their limitations when applied to data in the x->1 limit. We evaluate the numerical effects of TMCs on various structure functions, and compare fits to data with and without these corrections.Comment: 41 pages, 13 figures; minor updates to match published versio

Quantum interference and Klein tunneling in graphene heterojunctions

The observation of quantum conductance oscillations in mesoscopic systems has traditionally required the confinement of the carriers to a phase space of reduced dimensionality. While electron optics such as lensing and focusing have been demonstrated experimentally, building a collimated electron interferometer in two unconfined dimensions has remained a challenge due to the difficulty of creating electrostatic barriers that are sharp on the order of the electron wavelength. Here, we report the observation of conductance oscillations in extremely narrow graphene heterostructures where a resonant cavity is formed between two electrostatically created bipolar junctions. Analysis of the oscillations confirms that p-n junctions have a collimating effect on ballistically transmitted carriers. The phase shift observed in the conductance fringes at low magnetic fields is a signature of the perfect transmission of carriers normally incident on the junctions and thus constitutes a direct experimental observation of ``Klein Tunneling.''Comment: 13 pages and 6 figures including supplementary information. The paper has been modified in light of new theoretical results available at arXiv:0808.048