Homogeneous Fedosov Star Products on Cotangent Bundles I: Weyl and Standard Ordering with Differential Operator Representation

In this paper we construct homogeneous star products of Weyl type on every cotangent bundle $T^*Q$ by means of the Fedosov procedure using a symplectic torsion-free connection on $T^*Q$ homogeneous of degree zero with respect to the Liouville vector field. By a fibrewise equivalence transformation we construct a homogeneous Fedosov star product of standard ordered type equivalent to the homogeneous Fedosov star product of Weyl type. Representations for both star product algebras by differential operators on functions on $Q$ are constructed leading in the case of the standard ordered product to the usual standard ordering prescription for smooth complex-valued functions on $T^*Q$ polynomial in the momenta (where an arbitrary fixed torsion-free connection $\nabla_0$ on $Q$ is used). Motivated by the flat case $T^* R^n$ another homogeneous star product of Weyl type corresponding to the Weyl ordering prescription is constructed. The example of the cotangent bundle of an arbitrary Lie group is explicitly computed and the star product given by Gutt is rederived in our approach.Comment: 31 pages, LaTeX2e, no picture

On representations of star product algebras over cotangent spaces on Hermitian line bundles

For every formal power series $B=B_0 + \lambda B_1 + O(\lambda^2)$ of closed two-forms on a manifold $Q$ and every value of an ordering parameter $\kappa\in [0,1]$ we construct a concrete star product $\star^B_\kappa$ on the cotangent bundle $\pi : T^*Q\to Q$. The star product $\star^B_\kappa$ is associated to the formal symplectic form on $T^*Q$ given by the sum of the canonical symplectic form $\omega$ and the pull-back of $B$ to $T^*Q$. Deligne's characteristic class of $\star^B_\kappa$ is calculated and shown to coincide with the formal de Rham cohomology class of $\pi^*B$ divided by \im\lambda. Therefore, every star product on $T^*Q$ corresponding to the Poisson bracket induced by the symplectic form $\omega + \pi^*B_0$ is equivalent to some $\star^B_kappa$. It turns out that every $\star^B_kappa$ is strongly closed. In this paper we also construct and classify explicitly formal representations of the deformed algebra as well as operator representations given by a certain global symbol calculus for pseudodifferential operators on $Q$. Moreover, we show that the latter operator representations induce the formal representations by a certain Taylor expansion. We thereby obtain a compact formula for the WKB expansion.Comment: LaTeX2e, 38 pages, slight generalization of Theorem 4.4, minor typos correcte

Screening of future carbon storage sites – selecting the best spots

Subsurface carbon storage can occur in depleted oil and gas fields, in water-wet structures, or in open aquifers. All three types of storage sites present advantages and inconveniences, which will be reviewed in this talk. The selection of future sites for carbon storage balances storage capacity (how much CO2 can be stored), injectivity (how efficiently or fast CO2 can be stored), and containment risk (how safely CO2 can be stored). We present a rigorous uncertainty-based approach involving estimates of pore volume, pressure and temperature conditions and resulting fluid properties, and sealing and containment behaviour, to highlight areas with best potential for safe and effective carbon storage

Identifying suitable substrates for high-quality graphene-based heterostructures

We report on a scanning confocal Raman spectroscopy study investigating the strain-uniformity and the overall strain and doping of high-quality chemical vapour deposited (CVD) graphene-based heterostuctures on a large number of different substrate materials, including hexagonal boron nitride (hBN), transition metal dichalcogenides, silicon, different oxides and nitrides, as well as polymers. By applying a hBN-assisted, contamination free, dry transfer process for CVD graphene, high-quality heterostructures with low doping densities and low strain variations are assembled. The Raman spectra of these pristine heterostructures are sensitive to substrate-induced doping and strain variations and are thus used to probe the suitability of the substrate material for potential high-quality graphene devices. We find that the flatness of the substrate material is a key figure for gaining, or preserving high-quality graphene.Comment: 6 pages, 5 figure