Output Feedback Invariants

The paper is concerned with the problem of determining a complete set of invariants for output feedback. Using tools from geometric invariant theory it is shown that there exists a quasi-projective variety whose points parameterize the output feedback orbits in a unique way. If the McMillan degree $n\geq mp$, the product of number of inputs and number of outputs, then it is shown that in the closure of every feedback orbit there is exactly one nondegenerate system.Comment: 15 page

The Significance of the CC-Numerical Range and the Local CC-Numerical Range in Quantum Control and Quantum Information

This paper shows how C-numerical-range related new strucures may arise from practical problems in quantum control--and vice versa, how an understanding of these structures helps to tackle hot topics in quantum information. We start out with an overview on the role of C-numerical ranges in current research problems in quantum theory: the quantum mechanical task of maximising the projection of a point on the unitary orbit of an initial state onto a target state C relates to the C-numerical radius of A via maximising the trace function |\tr \{C^\dagger UAU^\dagger\}|. In quantum control of n qubits one may be interested (i) in having U\in SU(2^n) for the entire dynamics, or (ii) in restricting the dynamics to {\em local} operations on each qubit, i.e. to the n-fold tensor product SU(2)\otimes SU(2)\otimes >...\otimes SU(2). Interestingly, the latter then leads to a novel entity, the {\em local} C-numerical range W_{\rm loc}(C,A), whose intricate geometry is neither star-shaped nor simply connected in contrast to the conventional C-numerical range. This is shown in the accompanying paper (math-ph/0702005). We present novel applications of the C-numerical range in quantum control assisted by gradient flows on the local unitary group: (1) they serve as powerful tools for deciding whether a quantum interaction can be inverted in time (in a sense generalising Hahn's famous spin echo); (2) they allow for optimising witnesses of quantum entanglement. We conclude by relating the relative C-numerical range to problems of constrained quantum optimisation, for which we also give Lagrange-type gradient flow algorithms.Comment: update relating to math-ph/070200

Hamiltonian statistical mechanics

A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward those of the reference Hamiltonian. The nonlinear double-bracket equation governing the flow is such that the eigenvalues of the initial Hamiltonian remain unperturbed. The space of Hamiltonians is foliated by compact invariant subspaces, which permits the construction of statistical distributions over the Hamiltonians. In two dimensions, an explicit dynamical model is introduced, wherein the density function on the space of Hamiltonians approaches an equilibrium state characterised by the canonical ensemble. This is used to compute quenched and annealed averages of quantum observables.Comment: 8 pages, 2 figures, references adde

The contribution of oceanic methyl iodide to stratospheric iodine

We investigate the contribution of oceanic methyl iodide (CH3I) to the stratospheric iodine budget. Based on CH3I measurements from three tropical ship campaigns and the Lagrangian transport model FLEXPART, we provide a detailed analysis of CH3I transport from the ocean surface to the cold point in the upper tropical tropopause layer (TTL). While average oceanic emissions differ by less than 50% from campaign to campaign, the measurements show much stronger variations within each campaign. A positive correlation between the oceanic CH3I emissions and the efficiency of CH3I troposphere–stratosphere transport has been identified for some cruise sections. The mechanism of strong horizontal surface winds triggering large emissions on the one hand and being associated with tropical convective systems, such as developing typhoons, on the other hand, could explain the identified correlations. As a result of the simultaneous occurrence of large CH3I emissions and strong vertical uplift, localized maximum mixing ratios of 0.6 ppt CH3I at the cold point have been determined for observed peak emissions during the SHIVA (Stratospheric Ozone: Halogen Impacts in a Varying Atmosphere)-Sonne research vessel campaign in the coastal western Pacific. The other two campaigns give considerably smaller maxima of 0.1 ppt CH3I in the open western Pacific and 0.03 ppt in the coastal eastern Atlantic. In order to assess the representativeness of the large local mixing ratios, we use climatological emission scenarios to derive global upper air estimates of CH3I abundances. The model results are compared with available upper air measurements, including data from the recent ATTREX and HIPPO2 aircraft campaigns. In the eastern Pacific region, the location of the available measurement campaigns in the upper TTL, the comparisons give a good agreement, indicating that around 0.01 to 0.02 ppt of CH3I enter the stratosphere. However, other tropical regions that are subject to stronger convective activity show larger CH3I entrainment, e.g., 0.08 ppt in the western Pacific. Overall our model results give a tropical contribution of 0.04 ppt CH3I to the stratospheric iodine budget. The strong variations in the geographical distribution of CH3I entrainment suggest that currently available upper air measurements are not representative of global estimates and further campaigns will be necessary in order to better understand the CH3I contribution to stratospheric iodine

No association between islet cell antibodies and coxsackie B, mumps, rubella and cytomegalovirus antibodies in non-diabetic individuals aged 7–19 years

Viral antibodies were tested in a cohort of 44 isletcell antibody-positive individuals age 7–19 years, and 44 of their islet cell antibody-negative age and sex-matched classmates selected from a population study of 4208 pupils who had been screened for islet cell antibodies. Anti-coxsackie B1-5 IgM responses were detected in 14 of 44 (32%) of the islet cell antibody-positive subjects and in 7 of 44 (16%) control subjects. This difference did not reach the level of statistical significance. None of the islet cell antibody-positive subjects had specific IgM antibodies to mumps, rubella, or cytomegalovirus. There was also no increase in the prevalence or the mean titres of anti-mumps-IgG or IgA and anti-cytomegalovirus-IgG in islet cell antibody-positive subjects compared to control subjects. These results do not suggest any association between islet cell antibodies, and possibly insulitis, with recent mumps, rubella or cytomegalo virus infection. Further studies are required to clarify the relationship between islet cell antibodies and coxsackie B virus infections

Seasonal methane accumulation and release from a gas emission site in the central North Sea

We investigated dissolved methane distributions along a 6 km transect crossing active seep sites at 40 m water depth in the central North Sea. These investigations were done under conditions of thermal stratification in summer (July 2013) and homogenous water column in winter (January 2014). Dissolved methane accumulated below the seasonal thermocline in summer with a median concentration of 390 nM, whereas during winter, methane concentrations were typically much lower (median concentration of 22 nM). High-resolution methane analysis using an underwater mass-spectrometer confirmed our summer results and was used to document prevailing stratification over the tidal cycle. We contrast estimates of methane oxidation rates (from 0.1 to 4.0 nM day⁻¹) using the traditional approach scaled to methane concentrations with microbial turnover time values and suggest that the scaling to concentration may obscure the ecosystem microbial activity when comparing systems with different methane concentrations. Our measured and averaged rate constants (k') were on the order of 0.01 day−1, equivalent to a turnover time of 100 days, even when summer stratification led to enhanced methane concentrations in the bottom water. Consistent with these observations, we could not detect known methanotrophs and pmoA genes in water samples collected during both seasons. Estimated methane fluxes indicate that horizontal transport is the dominant process dispersing the methane plume. During periods of high wind speed (winter), more methane is lost to the atmosphere than oxidized in the water. Microbial oxidation seems of minor importance throughout the year.This work is part of the DFG project “Limitations of Marine Methane Oxidation” (MA 3961/2-1). This is the publisher’s final pdf. The published article is copyrighted by the author(s) and published by Copernicus Publications on behalf of the European Geosciences Union. The published article can be found at: http://www.biogeosciences.net/ For a previous discussion paper please see: http://hdl.handle.net/1957/5749

Seasonal methane accumulation and release from a gas emission site in the central North Sea

Hydroacoustic data document the occurrence of 5 flare clusters and several single flares from which bubbles rise through the entire water column from an active seep site at 40 m water depth in the central North Sea. We investigated the difference in dissolved methane distributions along a 6 km transect crossing this seep site during a period of seasonal summer stratification (July 2013) and a period of well mixed winter water column (January 2014). Dissolved methane accumulated below the seasonal thermocline in summer with a median concentration of 390 nM, whereas during winter, methane concentrations were much lower (median concentration of 22 nM) and punctually elevated due to bubble transport. High resolution methane analysis by an underwater mass-spectrometer confirmed our summer results and were used to document prevailing stratification over the tidal cycle. Although sufficient methane was available, microbial methane oxidation was limited during both seasons. Measured and averaged rate constants (k') using Michaelis Menten kinetics were on the order of 0.01 days⁻¹, equivalent to a turnover time of 100 days. Time series measurements indicated an uptake of only 5–6% of the gas after 4 days, and no known methanotrophs and pmoA-genes were detected. Estimated methane fluxes indicate that horizontal eddy transport rapidly disperses dissolved methane, vertical transport becomes dominant during phases of high wind speeds, and relative to these processes, microbial methane oxidation appears to be comparably low. To bridge the discrete field data we developed a 1-D seasonal model using available year-long records of wind speed, surface temperature and thermocline depth. The model simulations show a peak release of methane at the beginning of fall when the water column becomes mixed. Consistent with our field data, inclusion of microbial methane oxidation does not change the model results significantly, thus microbial oxidation appears to be not sufficient to notably reduce methane during summer stratification before the peak release in fall.This work is part of the DFG project “Limitations of Marine Methane Oxidation” (MA 3961/2-1). This discussion paper has been under review for the journal Biogeosciences (BG). Please refer to the corresponding final paper in BG. The published article is copyrighted by the author(s) and published by Copernicus Publications on behalf of the European Geosciences Union. The published article can be found at: http://www.biogeosciences.net/ The final revised paper is available at: http://hdl.handle.net/1957/5749