Quantum stochastic convolution cocycles II

Schuermann's theory of quantum Levy processes, and more generally the theory of quantum stochastic convolution cocycles, is extended to the topological context of compact quantum groups and operator space coalgebras. Quantum stochastic convolution cocycles on a C*-hyperbialgebra, which are Markov-regular, completely positive and contractive, are shown to satisfy coalgebraic quantum stochastic differential equations with completely bounded coefficients, and the structure of their stochastic generators is obtained. Automatic complete boundedness of a class of derivations is established, leading to a characterisation of the stochastic generators of *-homomorphic convolution cocycles on a C*-bialgebra. Two tentative definitions of quantum Levy process on a compact quantum group are given and, with respect to both of these, it is shown that an equivalent process on Fock space may be reconstructed from the generator of the quantum Levy process. In the examples presented, connection to the algebraic theory is emphasised by a focus on full compact quantum groups.Comment: 32 pages, expanded introduction and updated references. The revised version will appear in Communications in Mathematical Physic

Quantum stochastic convolution cocycles III

Every Markov-regular quantum Levy process on a multiplier C*-bialgebra is shown to be equivalent to one governed by a quantum stochastic differential equation, and the generating functionals of norm-continuous convolution semigroups on a multiplier C*-bialgebra are then completely characterised. These results are achieved by extending the theory of quantum Levy processes on a compact quantum group, and more generally quantum stochastic convolution cocycles on a C*-bialgebra, to locally compact quantum groups and multiplier C*-bialgebras. Strict extension results obtained by Kustermans, together with automatic strictness properties developed here, are exploited to obtain existence and uniqueness for coalgebraic quantum stochastic differential equations in this setting. Then, working in the universal enveloping von Neumann bialgebra, we characterise the stochastic generators of Markov-regular, *-homomorphic (respectively completely positive and contractive), quantum stochastic convolution cocycles.Comment: 20 pages; v2 corrects some typos and no longer contains a section on quantum random walk approximations, which will now appear as a separate submission. The article will appear in the Mathematische Annale

Automated acoustic intensity measurements and the effect of gear tooth profile on noise

Acoustic intensity measurements were made at NASA Lewis Research Center on a spur gear test apparatus. The measurements were obtained with the Robotic Acoustic Intensity Measurement System developed by Cleveland State University. This system provided dense spatial positioning, and was calibrated against a high quality acoustic intensity system. The measured gear noise compared gearsets having two different tooth profiles. The tests evaluated the sound field of the different gears for two speeds and three loads. The experimental results showed that gear tooth profile had a major effect on measured noise. Load and speed were found to have an effect on noise also

An Improved Red Spectrum of the Methane or T-dwarf SDSS 1624+0029: Role of the Alkali Metals

A Keck~II low resolution spectrum shortward of ome-micron is presented for SDSS 1624+0029, the first field methane or T dwarf discovered in the Sloan Digital Sky Survey. Significant flux is detected down to the spectrum's short wavelength limit of 6200\AA. The spectrum exhibits a broad absorption feature centered at 7700\AA, which we interpret as the K~I 7665/7699 resonance doublet. The observed flux declines shortward of 7000\AA, due most likely to the red wing of the Na~I doublet. Both Cs~I doublet lines are detected more strongly than in an earlier red spectrum. Neither Li~I absorption nor H$\alpha$ emission are detected. An exploratory model fit to the spectrum suggests that the shape of the red spectrum can be primarily accounted for by the broad wings of the K~I and Na~I doublets. This behavior is consistent with the argument proffered by Burrows, Marley and Sharp that strong alkali absorption is principally responsible for depressing T dwarf spectra shortward of 1$\mu$m. In particular, there seems no compelling reason at this time to introduce dust or an additional opacity source in the atmosphere of the SDSS object. The width of the K~I and strengths of the Cs~I lines also indicate that the Sloan object is warmer than Gl~229B.Comment: accepted March 3, 2000 for Ap.J. Letters, LaTeX, 2 figure

Integrable subsystem of Yang--Mills dilaton theory

With the help of the Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field, we find an integrable subsystem of SU(2) Yang-Mills theory coupled to the dilaton. Here integrability means the existence of infinitely many symmetries and infinitely many conserved currents. Further, we construct infinitely many static solutions of this integrable subsystem. These solutions can be identified with certain limiting solutions of the full system, which have been found previously in the context of numerical investigations of the Yang-Mills dilaton theory. In addition, we derive a Bogomolny bound for the integrable subsystem and show that our static solutions are, in fact, Bogomolny solutions. This explains the linear growth of their energies with the topological charge, which has been observed previously. Finally, we discuss some generalisations.Comment: 25 pages, LaTex. Version 3: appendix added where the equivalence of the field equations for the full model and the submodel is demonstrated; references and some comments adde

The Class Size Controversy

[Excerpt] When we ask whether class size matters for achievement, it is essential to ask also, how class size matters. This is important for three reasons. First, if we can observe not only achievement differences, but also the mechanisms through which the differences are produced, this will increase our confidence that the differences are real, and not an artifact of some unmeasured or inadequately controlled condition. Second, the effects of class size may vary in different circumstances, and identifying how class size affects achievement will help us to understand why the effects of class size are variable. Third, the potential benefits of class size reduction may be greater than what we observe. For example, suppose class size reductions aid achievement, but only when teachers modify instructional practices to take advantage of the smaller classes. If a few teachers make such modifications, but most do not, then understanding how class size affects achievement in some cases will help reveal its potential effects, even if the potential is generally unrealized

Performance assessment of tariff-based air source heat pump load shifting in a UK detached dwelling featuring phase change-enhanced buffering

Using a detailed building simulation model, the amount of thermal buffering, with and without phase change material (PCM), needed to time-shift an air source heat pump's operation to off-peak periods, as defined by the UK 'Economy 10' tariff, was investigated for a typical UK detached dwelling. The performance of the buffered system was compared to the case with no load shifting and with no thermal buffering. Additionally, the load shifting of a population of buffered heat pumps to off-peak periods was simulated and the resulting change in the peak demand on the electricity network was assessed. The results from this study indicate that 1000 L of hot water buffering or 500 L of PCM-enhanced hot water buffering was required to move the operation of the heat pump fully to off-peak periods, without adversely affecting the provision of space heating and hot water for the end user. The work also highlights that buffering and load shifting increased the heat pump's electrical demand by over 60% leading to increased cost to the end user and increased CO2 emissions (depending on the electricity tariff applied and time varying CO2 intensity of the electricity generation mix, respectively). The study also highlights that the load-shifting of populations of buffered heat pumps wholly to off-peak periods using crude instruments such as tariffs increased the peak loading on the electrical network by over 50% rather than reducing it and that careful consideration is needed as to how the load shifting of a group of heat pumps is orchestrated

THE DYSON-SCHWINGER EQUATION FOR A MODEL WITH INSTANTONS - THE SCHWINGER MODEL

Using the exact path integral solution of the Schwinger model -- a model where instantons are present -- the Dyson-Schwinger equation is shown to hold by explicit computation. It turns out that the Dyson-Schwinger equation separately holds for every instanton sector. This is due to Theta-invariance of the Schwinger model.Comment: LATEX file 11 pages, no figure

Experimental semi-device-independent certification of entangled measurements

Certifying the entanglement of quantum states with Bell inequalities allows one to guarantee the security of quantum information protocols independently of imperfections in the measuring devices. Here we present a similar procedure for witnessing entangled measurements, which play a central role in many quantum information tasks. Our procedure is termed semi-device-independent, as it uses uncharacterized quantum preparations of fixed Hilbert space dimension. Using a photonic setup, we experimentally certify an entangled measurement using measurement statistics only. We also apply our techniques to certify unentangled but nevertheless inherently quantum measurements.Comment: 7 pages, 2 figure