Divergence-free approach for obtaining decompositions of quantum-optical processes

Operator-sum representations of quantum channels can be obtained by applying the channel to one subsystem of a maximally entangled state and deploying the channel-state isomorphism. However, for continuous-variable systems, such schemes contain natural divergences since the maximally entangled state is ill-defined. We introduce a method that avoids such divergences by utilizing finitely entangled (squeezed) states and then taking the limit of arbitrary large squeezing. Using this method we derive an operator-sum representation for all single-mode bosonic Gaussian channels where a unique feature is that both quantum-limited and noisy channels are treated on an equal footing. This technique facilitates a proof that the rank-one Kraus decomposition for Gaussian channels at its respective entanglement-breaking thresholds, obtained in the overcomplete coherent state basis, is unique. The methods could have applications to simulation of continuous-variable channels.Comment: 18 pages (8 + appendices), 4 figs. V2: close to published version, dropped Sec.VI of v1 to be expanded elsewher

Galactic dust polarized emission at high latitudes and CMB polarization

We estimate the dust polarized emission in our galaxy at high galactic latitudes, which is the dominant foreground for measuring CMB polarization using the high frequency instrument (HFI) aboard Planck surveyor. We compare it with the level of CMB polarization and conclude that, for angular scales $\le 1^{\circ}$, the scalar-induced CMB polarization and temperature-polarization cross-correlation are much larger than the foreground level at $\nu \simeq 100 GHz$. The tensor-induced signals seem to be at best comparable to the foreground level.}Comment: Latex document, 4 pages, 2 figures, to appear in "Fundamental parameters in Cosmology", Rencontres de Moriond, 199

QCD corrections to the hadronic production of a heavy quark pair and a W-boson including decay correlations

We perform an analytic calculation of the one-loop amplitude for the W-boson mediated process 0 \to d u-bar Q Q-bar l-bar l, retaining the mass for the quark Q. The momentum of each of the massive quarks is expressed as the sum of two massless momenta and the corresponding heavy quark spinor is expressed as a sum of two massless spinors. Using a special choice for the heavy quark spinors we obtain analytic expressions for the one-loop amplitudes which are amenable to fast numerical evaluation. The full next-to-leading order (NLO) calculation of hadron+hadron \to W(\to e nu) b b-bar with massive b-quarks is included in the program MCFM. A comparison is performed with previous published work.Comment: 45 pages, 17 figure

Hamilton's Turns for the Lorentz Group

Hamilton in the course of his studies on quaternions came up with an elegant geometric picture for the group SU(2). In this picture the group elements are represented by ``turns'', which are equivalence classes of directed great circle arcs on the unit sphere $S^2$, in such a manner that the rule for composition of group elements takes the form of the familiar parallelogram law for the Euclidean translation group. It is only recently that this construction has been generalized to the simplest noncompact group $SU(1,1) = Sp(2, R) = SL(2,R)$, the double cover of SO(2,1). The present work develops a theory of turns for $SL(2,C)$, the double and universal cover of SO(3,1) and $SO(3,C)$, rendering a geometric representation in the spirit of Hamilton available for all low dimensional semisimple Lie groups of interest in physics. The geometric construction is illustrated through application to polar decomposition, and to the composition of Lorentz boosts and the resulting Wigner or Thomas rotation.Comment: 13 pages, Late

Extended observables in theories with constraints

In a classical Hamiltonian theory with second class constraints the phase space functions on the constraint surface are observables. We give general formulas for extended observables, which are expressions representing the observables in the enveloping unconstrained phase space. These expressions satisfy in the unconstrained phase space a Poisson algebra of the same form as the Dirac bracket algebra of the observables on the constraint surface. The general formulas involve new differential operators that differentiate the Dirac bracket. Similar extended observables are also constructed for theories with first class constraints which, however, are gauge dependent. For such theories one may also construct gauge invariant extensions with similar properties. Whenever extended observables exist the theory is expected to allow for a covariant quantization. A mapping procedure is proposed for covariant quantization of theories with second class constraints.Comment: 26 pages, Latexfile,Minor misprints on page 4 are correcte

Delivering organisational adaptation through legislative mechanisms: Evidence from the Adaptation Reporting Power (Climate Change Act 2008)

There is increasing recognition that organisations, particularly in key infrastructure sectors, are potentially vulnerable to climate change and extreme weather events, and require organisational responses to ensure they are resilient and adaptive. However, detailed evidence of how adaptation is facilitated, implemented and reported, particularly through legislative mechanisms is lacking. The United Kingdom Climate Change Act (2008), introduced the Adaptation Reporting Power, enabling the Government to direct so-called reporting authorities to report their climate change risks and adaptation plans. We describe the authors' unique role and experience supporting the Department for Environment, Food and Rural Affairs (Defra) during the Adaptation Reporting Power's first round. An evaluation framework, used to review the adaptation reports, is presented alongside evidence on how the process provides new insights into adaptation activities and triggered organisational change in 78% of reporting authorities, including the embedding of climate risk and adaptation issues. The role of legislative mechanisms and risk-based approaches in driving and delivering adaptation is discussed alongside future research needs, including the development of organisational maturity models to determine resilient and well adapting organisations. The Adaptation Reporting Power process provides a basis for similar initiatives in other countries, although a clear engagement strategy to ensure buy-in to the process and research on its long-term legacy, including the potential merits of voluntary approaches, is required

[CII] 158μ\mum and [NII] 205μ\mum emission from IC 342 - Disentangling the emission from ionized and photo-dissociated regions

Aims: We investigate how much of the [CII] emission in the nucleus of the nearby spiral galaxy IC 342 is contributed by PDRs and by the ionized gas. We examine the spatial variations of starburst/PDR activity and study the correlation of the [CII] line with the [NII] 205{\textmu}m emission line coming exclusively from the HII regions. Methods: We present small maps of [CII] and [NII] lines recently observed with the GREAT receiver on board SOFIA. In particular we present a super-resolution method to derive how unresolved, kinematically correlated structures in the beam contribute to the observed line shapes. Results: We find that the emission coming from the ionized gas shows a kinematic component in addition to the general Doppler signature of the molecular gas. We interpret this as the signature of two bi-polar lobes of ionized gas expanding out of the galactic plane. We then show how this requires an adaptation of our understanding of the geometrical structure of the nucleus of IC~342. Examining the starburst activity we find ratios $I([CII])/I(^{12}\mathrm{CO} (1-0))$ between 400 and 1800 in energy units. Applying predictions from numerical models of HII and PDR regions to derive the contribution from the ionized phase to the total [CII] emission we find that 35-90% of the observed [CII] intensity stems from the ionized gas if both phases contribute. Averaged over the central few hundred parsec we find for the [CII] contribution a HII-to-PDR ratio of 70:30. Conclusions: The ionized gas in the center of IC 342 contributes more strongly to the overall [CII] emission than is commonly observed on larger scales and than is predicted. Kinematic analysis shows that the majority of the [CII] emission is related to the strong but embedded star formation in the nuclear molecular ring and only marginally emitted from the expanding bi-polar lobes of ionized gas.Comment: 20 pages spectra available online: http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/ submitted to and accepted by A&

The quantum correlation between the selection of the problem and that of the solution sheds light on the mechanism of the quantum speed up

In classical problem solving, there is of course correlation between the selection of the problem on the part of Bob (the problem setter) and that of the solution on the part of Alice (the problem solver). In quantum problem solving, this correlation becomes quantum. This means that Alice contributes to selecting 50% of the information that specifies the problem. As the solution is a function of the problem, this gives to Alice advanced knowledge of 50% of the information that specifies the solution. Both the quadratic and exponential speed ups are explained by the fact that quantum algorithms start from this advanced knowledge.Comment: Earlier version submitted to QIP 2011. Further clarified section 1, "Outline of the argument", submitted to Phys Rev A, 16 page

A Fully Calibrated Generalized CES Programming Model of Agricultural Supply

The use of prior information on supply elasticities to calibrate programming models of agricultural supply has been advocated repeatedly in the recent literature (Heckelei and Britz 2005). Yet, Mérel and Bucaram (2009) have shown that the dual goal of calibrating such models to a reference allocation while replicating an exogenous set of supply elasticities is not always feasible. This article lays out the methodological foundation to exactly calibrate programming models of agricultural supply using generalized CES production functions. We formally derive the necessary and sufficient conditions under which such models can be calibrated to replicate the reference allocation while displaying crop-specific supply responses that are consistent with prior information. When it exists, the solution to the exact calibration problem is unique. From a microeconomic perspective, the generalized CES model is preferable to quadratic models that have been used extensively in policy analysis since the publication of Howitt’s (1995) Positive Mathematical Programming. The two types of specifications are also compared on the basis of their flexibility towards calibration, and it is shown that, provided myopic calibration is feasible, the generalized CES model can calibrate larger sets of supply elasticities than its quadratic counterpart. Our calibration criterion has relevance both for calibrated positive mathematical programming models and for “well-posed” models estimated through generalized maximum entropy following Heckelei and Wolff (2003), where it is deemed appropriate to include prior information regarding the value of own-price supply elasticities.Positive mathematical programming, generalized CES, supply elasticities, Crop Production/Industries, Production Economics,