The Schroedinger operator as a generalized Laplacian

The Schroedinger operators on the Newtonian space-time are defined in a way which make them independent on the class of inertial observers. In this picture the Schroedinger operators act not on functions on the space-time but on sections of certain one-dimensional complex vector bundle -- the Schroedinger line bundle. This line bundle has trivializations indexed by inertial observers and is associated with an U(1)-principal bundle with an analogous list of trivializations -- the Schroedinger principal bundle. For the Schroedinger principal bundle a natural differential calculus for `wave forms' is developed that leads to a natural generalization of the concept of Laplace-Beltrami operator associated with a pseudo-Riemannian metric. The free Schroedinger operator turns out to be the Laplace-Beltrami operator associated with a naturally distinguished invariant pseudo-Riemannian metric on the Schroedinger principal bundle. The presented framework is proven to be strictly related to the frame-independent formulation of analytical Newtonian mechanics and Hamilton-Jacobi equations, that makes a bridge between the classical and quantum theory.Comment: 19 pages, a remark, an example and references added - the version to appear in J. Phys. A: Math. and Theo

The graded Jacobi algebras and (co)homology

Jacobi algebroids (i.e. `Jacobi versions' of Lie algebroids) are studied in the context of graded Jacobi brackets on graded commutative algebras. This unifies varios concepts of graded Lie structures in geometry and physics. A method of describing such structures by classical Lie algebroids via certain gauging (in the spirit of E.Witten's gauging of exterior derivative) is developed. One constructs a corresponding Cartan differential calculus (graded commutative one) in a natural manner. This, in turn, gives canonical generating operators for triangular Jacobi algebroids. One gets, in particular, the Lichnerowicz-Jacobi homology operators associated with classical Jacobi structures. Courant-Jacobi brackets are obtained in a similar way and use to define an abstract notion of a Courant-Jacobi algebroid and Dirac-Jacobi structure. All this offers a new flavour in understanding the Batalin-Vilkovisky formalism.Comment: 20 pages, a few typos corrected; final version to be published in J. Phys. A: Math. Ge

Jet production in charged current deep inelastic e⁺p scatteringat HERA

The production rates and substructure of jets have been studied in charged current deep inelastic e⁺p scattering for Q² > 200 GeV² with the ZEUS detector at HERA using an integrated luminosity of 110.5 pb⁻¹. Inclusive jet cross sections are presented for jets with transverse energies E_{T}^{jet} > 5 GeV. Measurements of the mean subjet multiplicity, 〈n_{sbj}〉, of the inclusive jet sample are presented. Predictions based on parton-shower Monte Carlo models and next-to-leading-order QCD calculations are compared to the measurements. The value of α_{s} (M_{z}), determined from 〈n_{sbj}〉 at y_{cut} = 10⁻² for jets with 25 < E_{T}^{jet} < 119 GeV, is α_{s} (M_{z}) = 0.1202 ± 0.0052 (stat.)_{-0.0019}^{+0.0060} (syst.)_{-0.0053}^{+0.0065} (th.). The mean subjet multiplicity as a function of Q² is found to be consistent with that measured in NC DIS

Multijet production in neutral current deep inelastic scattering at HERA and determination of α_{s}

Multijet production rates in neutral current deep inelastic scattering have been measured in the range of exchanged boson virtualities 10 5 GeV and –1 < η_{LAB}^{jet} < 2.5. Next-to-leading-order QCD calculations describe the data well. The value of the strong coupling constant α_{s} (M_{z}), determined from the ratio of the trijet to dijet cross sections, is α_{s} (M_{z}) = 0.1179 ± 0.0013 (stat.)_{-0.0046}^{+0.0028}(exp.)_{-0.0046}^{+0.0028}(th.)

Length versus radius relationship for ZnO nanowires grown via vapour phase transport

We model the growth of ZnO nanowires via vapour phase transport and examine the relationship predicted between the nanowire length and radius. The model predicts that the lengths of the nanowires increase with decreasing nanowire radii. This prediction is in very good agreement with experimental data from a variety of nanowire samples, including samples showing a broad range of nanowire radii and samples grown using a lithographic technique to constrain the nanowire radius. The close agreement of the model and the experimental data strongly support supporting the inclusion of a surface diffusion term in the model for the incorporation of species into a growing nanowire

Theoretical analysis of nucleation and growth of ZnO nanostructures in vapour phase transport growth

This paper discusses the growth atmosphere, condensing species and nucleation conditions relevant to vapour phase transport growth of ZnO nanostructures, including the molecular parameters and thermodynamics of the gas phase ZnO molecule and its importance compared to atomic Zn and molecular O2. The partial pressure of molecular ZnO in a Zn/O2 mix at normal ZnO growth temperatures is 6x10^-7 of the Zn partial pressures. In typical vapour phase transport growth conditions, using carbothermal reduction, the Zn vapour is always undersaturated while the ZnO vapour is always supersaturated. In the case of the ZnO vapour, our analysis suggests that the barrier to homogeneous nucleation (or heterogeneous nucleation at unseeded/uncatalysed areas of the substrates) is too large for nucleation of this species to take place, which is consistent with experimental evidence that nanostructures will not grow on unseeded areas of substrates. In the presence of suitable accommodation sites, due to ZnO seeds, growth can occur via Zn vapour condensation (followed by oxidation) and via direct condensation of molecular ZnO (whose flux at the surface, although less than that of Zn vapour, is still sufficient to yield an appreciable nanostructure deposit). The balance between these two condensing species is likely to be a sensitive function of growth parameters and could explain both the diversity of reported nanostructure morphologies and the challenges to be faced in developing reproducible and scalable growth systems for specific applicable morphologies

High-E_T dijet photoproduction at HERA

The cross section for high-E_T dijet production in photoproduction has been measured with the ZEUS detector at HERA using an integrated luminosity of 81.8 pb-1. The events were required to have a virtuality of the incoming photon, Q^2, of less than 1 GeV^2 and a photon-proton centre-of-mass energy in the range 142 < W < 293 GeV. Events were selected if at least two jets satisfied the transverse-energy requirements of E_T(jet1) > 20 GeV and E_T(jet2) > 15 GeV and pseudorapidity requirements of -1 < eta(jet1,2) < 3, with at least one of the jets satisfying -1 < eta(jet) < 2.5. The measurements show sensitivity to the parton distributions in the photon and proton and effects beyond next-to-leading order in QCD. Hence these data can be used to constrain further the parton densities in the proton and photon.Comment: 36 pages, 13 figures, 20 tables, including minor revisions from referees. Accepted by Phys. Rev.

Search for direct stau production in events with two hadronic tau-leptons in root s=13 TeV pp collisions with the ATLAS detector

A search for the direct production of the supersymmetric partners ofτ-leptons (staus) in final stateswith two hadronically decayingτ-leptons is presented. The analysis uses a dataset of pp collisions corresponding to an integrated luminosity of139fb−1, recorded with the ATLAS detector at the LargeHadron Collider at a center-of-mass energy of 13 TeV. No significant deviation from the expected StandardModel background is observed. Limits are derived in scenarios of direct production of stau pairs with eachstau decaying into the stable lightest neutralino and oneτ-lepton in simplified models where the two staumass eigenstates are degenerate. Stau masses from 120 GeV to 390 GeV are excluded at 95% confidencelevel for a massless lightest neutralino