Spin in the path integral: anti-commuting versus commuting variables

We discuss the equivalence between the path integral representations of spin dynamics for anti-commuting (Grassmann) and commuting variables and establish a bosonization dictionary for both generators of spin and single fermion operators. The content of this construction in terms of the representations of the spin algebra is discussed in the path integral setting. Finally it is shown how a `free field realization' (Dyson mapping) can be constructed in the path integral.Comment: 9 pages, Late

Quantum phase transitions from topology in momentum space

Many quantum condensed matter systems are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, physics which emerges in the low-energy corner does not depend on the complicated details of the system and is relatively simple. It is determined by the nodes in the fermionic spectrum, which are protected by topology in momentum space (in some cases, in combination with the vacuum symmetry). Close to the nodes the behavior of the system becomes universal; and the universality classes are determined by the toplogical invariants in momentum space. When one changes the parameters of the system, the transitions are expected to occur between the vacua with the same symmetry but which belong to different universality classes. Different types of quantum phase transitions governed by topology in momentum space are discussed in this Chapter. They involve Fermi surfaces, Fermi points, Fermi lines, and also the topological transitions between the fully gapped states. The consideration based on the momentum space topology of the Green's function is general and is applicable to the vacua of relativistic quantum fields. This is illustrated by the possible quantum phase transition governed by topology of nodes in the spectrum of elementary particles of Standard Model.Comment: 45 pages, 17 figures, 83 references, Chapter for the book "Quantum Simulations via Analogues: From Phase Transitions to Black Holes", to appear in Springer lecture notes in physics (LNP

Graphene based superconducting quantum point contacts

We investigate the Josephson effect in the graphene nanoribbons of length $L$ smaller than the superconducting coherence length and an arbitrary width $W$. We find that in contrast to an ordinary superconducting quantum point contact (SQPC) the critical supercurrent $I_c$ is not quantized for the nanoribbons with smooth and armchair edges. For a low concentration of the carriers $I_c$ decreases monotonically with lowering $W/L$ and tends to a constant minimum for a narrow nanoribbon with $W\lesssim L$. The minimum $I_c$ is zero for the smooth edges but $e\Delta_{0}/\hbar$ for the armchair edges. At higher concentrations of the carriers this monotonic variation acquires a series of peaks. Further analysis of the current-phase relation and the Josephson coupling strength $I_cR_N$ in terms of $W/L$ and the concentration of carriers revels significant differences with those of an ordinary SQPC. On the other hand for a zigzag nanoribbon we find that, similar to an ordinary SQPC, $I_c$ is quantized but to the half-integer values $(n+1/2)4e\Delta_{0}/\hbar$.Comment: 8 pages, 5 figure

Vacuum structure of Toroidal Carbon Nanotubes

Low energy excitations in carbon nanotubes can be described by an effective field theory of two components spinor. It is pointed out that the chiral anomaly in 1+1 dimensions should be observed in a metallic toroidal carbon nanotube on a planar geometry with varying magnetic field. We propose an experimental setup for studying this quantum effect. We also analyze the vacuum structure of the metallic toroidal carbon nanotube including the Coulomb interactions and discuss some effects of external charges on the vacuum.Comment: 10 pages, 11 figure

Abelian-Projected Effective Gauge Theory of QCD with Asymptotic Freedom and Quark Confinement

We give an outline of a recent proof that the low-energy effective gauge theory exhibiting quark confinement due to magnetic monopole condensation can be derived from QCD without any specific assumption. We emphasize that the low-energy effective abelian gauge theories obtained here give the dual description of the same physics in the low-energy region. They show that the QCD vacuum is nothing but the dual (type II) superconductor.Comment: 15 pages, Latex, no figures, Talk given at YKIS'97, Non-perturbative QCD, Kyot

Abelian-Projected Effective Gauge Theory of QCD with Asymptotic Freedom and Quark Confinement

Starting from SU(2) Yang-Mills theory in 3+1 dimensions, we prove that the abelian-projected effective gauge theories are written in terms of the maximal abelian gauge field and the dual abelian gauge field interacting with monopole current. This is performed by integrating out all the remaining non-Abelian gauge field belonging to SU(2)/U(1). We show that the resulting abelian gauge theory recovers exactly the same one-loop beta function as the original Yang-Mills theory. Moreover, the dual abelian gauge field becomes massive if the monopole condensation occurs. This result supports the dual superconductor scenario for quark confinement in QCD. We give a criterion of dual superconductivity and point out that the monopole condensation can be estimated from the classical instanton configuration. Therefore there can exist the effective abelian gauge theory which shows both asymptotic freedom and quark confinement based on the dual Meissner mechanism. Inclusion of arbitrary number of fermion flavors is straightforward in this approach. Some implications to lower dimensional case will also be discussed.Comment: 39 pages, Latex, no figures, (2.2, 4.1, 4.3 are modified; 4.4, Appendices A,B,C and references are added. No change in conclusion

Origin and Evolution of Saturn's Ring System

The origin and long-term evolution of Saturn's rings is still an unsolved problem in modern planetary science. In this chapter we review the current state of our knowledge on this long-standing question for the main rings (A, Cassini Division, B, C), the F Ring, and the diffuse rings (E and G). During the Voyager era, models of evolutionary processes affecting the rings on long time scales (erosion, viscous spreading, accretion, ballistic transport, etc.) had suggested that Saturn's rings are not older than 100 My. In addition, Saturn's large system of diffuse rings has been thought to be the result of material loss from one or more of Saturn's satellites. In the Cassini era, high spatial and spectral resolution data have allowed progress to be made on some of these questions. Discoveries such as the ''propellers'' in the A ring, the shape of ring-embedded moonlets, the clumps in the F Ring, and Enceladus' plume provide new constraints on evolutionary processes in Saturn's rings. At the same time, advances in numerical simulations over the last 20 years have opened the way to realistic models of the rings's fine scale structure, and progress in our understanding of the formation of the Solar System provides a better-defined historical context in which to understand ring formation. All these elements have important implications for the origin and long-term evolution of Saturn's rings. They strengthen the idea that Saturn's rings are very dynamical and rapidly evolving, while new arguments suggest that the rings could be older than previously believed, provided that they are regularly renewed. Key evolutionary processes, timescales and possible scenarios for the rings's origin are reviewed in the light of tComment: Chapter 17 of the book ''Saturn After Cassini-Huygens'' Saturn from Cassini-Huygens, Dougherty, M.K.; Esposito, L.W.; Krimigis, S.M. (Ed.) (2009) 537-57

Measurement of the p-pbar -> Wgamma + X cross section at sqrt(s) = 1.96 TeV and WWgamma anomalous coupling limits

The WWgamma triple gauge boson coupling parameters are studied using p-pbar -> l nu gamma + X (l = e,mu) events at sqrt(s) = 1.96 TeV. The data were collected with the DO detector from an integrated luminosity of 162 pb^{-1} delivered by the Fermilab Tevatron Collider. The cross section times branching fraction for p-pbar -> W(gamma) + X -> l nu gamma + X with E_T^{gamma} > 8 GeV and Delta R_{l gamma} > 0.7 is 14.8 +/- 1.6 (stat) +/- 1.0 (syst) +/- 1.0 (lum) pb. The one-dimensional 95% confidence level limits on anomalous couplings are -0.88 < Delta kappa_{gamma} < 0.96 and -0.20 < lambda_{gamma} < 0.20.Comment: Submitted to Phys. Rev. D Rapid Communication

Measurement of the ttbar Production Cross Section in ppbar Collisions at sqrt{s} = 1.96 TeV using Kinematic Characteristics of Lepton + Jets Events

We present a measurement of the top quark pair ttbar production cross section in ppbar collisions at a center-of-mass energy of 1.96 TeV using 230 pb**{-1} of data collected by the DO detector at the Fermilab Tevatron Collider. We select events with one charged lepton (electron or muon), large missing transverse energy, and at least four jets, and extract the ttbar content of the sample based on the kinematic characteristics of the events. For a top quark mass of 175 GeV, we measure sigma(ttbar) = 6.7 {+1.4-1.3} (stat) {+1.6- 1.1} (syst) +/-0.4 (lumi) pb, in good agreement with the standard model prediction.Comment: submitted to Phys.Rev.Let

Measurement of the ttbar Production Cross Section in ppbar Collisions at sqrt(s)=1.96 TeV using Lepton + Jets Events with Lifetime b-tagging

We present a measurement of the top quark pair ($t\bar{t}$) production cross section ($\sigma_{t\bar{t}}$) in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV using 230 pb$^{-1}$ of data collected by the D0 experiment at the Fermilab Tevatron Collider. We select events with one charged lepton (electron or muon), missing transverse energy, and jets in the final state. We employ lifetime-based b-jet identification techniques to further enhance the $t\bar{t}$ purity of the selected sample. For a top quark mass of 175 GeV, we measure $\sigma_{t\bar{t}}=8.6^{+1.6}_{-1.5}(stat.+syst.)\pm 0.6(lumi.)$ pb, in agreement with the standard model expectation.Comment: 7 pages, 2 figures, 3 tables Submitted to Phys.Rev.Let