Kakutani Dichotomy on Free States

Two quasi-free states on a CAR or CCR algebra are shown to generate quasi-equivalent representations unless they are disjoint.Comment: 12 page

The impact of wastewater treatment effluent on Crocodile River quality in Ehlanzeni District, Mpumalanga Province, South Africa

Excessive discharge of poorly treated effluent has impacted global water resource systems intensely. The declining state of wastewater treatment plants (WWTPs) is a significant source of pollution in water resources. There is evidence of water resource quality deterioration in natural environments caused by effluent discharges. We assessed the impact of wastewater treatment effluent on the quality of the Crocodile River. For spatial distribution, we collected data from three WWTPs discharging effluent into the Crocodile River and from three points situated downstream of each WWTP. Physicochemical and microbiological parameters such as pH, electrical conductivity, chemical oxygen demand, phosphates, nitrates, ammonia, and Escherichia coli were analysed using standard methods of the American Public Health Association. The water quality index was also calculated to give an overall indication of pollution within the catchment. The results show that WWTPs were not complying with the effluent standards set out in their water use licence. The WWTP effluent had a negative impact on downstream water quality, with the water quality index indicating low quality of discharged effluent. It is recommended that a regular and consistent water resource quality monitoring programme be implemented, particularly in areas where effluent discharges are prevalent. Significance:In many African nations, water pollution is a serious problem that may be traced to a variety of sources. Surface water pollution has adverse effects on aquatic ecosystems and reduces the availability of clean water. In most semi-arid to dry southern African regions (e.g. South Africa), water scarcity is a significant concern. In these regions, water is a vital resource that must be protected at all times, given that the inadequate infrastructure of wastewater treatment facilities adds to the decline in South Africa’s water quality standard

Notes on the Geology of Jackson County, Iowa

Outcrops of the Maquoketa shale are limited to the eastern portions of Jackson County. Their position is controlled chiefly by the gentle regional dip to the southwest which in the north brings the basal beds and the underlying Galena formation to the surface and to the south in Clinton County causes the uppermost Maquoketa beds to disappear under the Silurian. This dip also allows the Maquoketa outcrops to extend progressively farther upstream in the beds of the northern east-flowing creeks

Applications of Canonical Transformations

Canonical transformations are defined and discussed along with the exponential, the coherent and the ultracoherent vectors. It is shown that the single-mode and the $n$-mode squeezing operators are elements of the group of canonical transformations. An application of canonical transformations is made, in the context of open quantum systems, by studying the effect of squeezing of the bath on the decoherence properties of the system. Two cases are analyzed. In the first case the bath consists of a massless bosonic field with the bath reference states being the squeezed vacuum states and squeezed thermal states while in the second case a system consisting of a harmonic oscillator interacting with a bath of harmonic oscillators is analyzed with the bath being initially in a squeezed thermal state.Comment: 14 page

Does pulmonary rehabilitation address cardiovascular risk factors in patients with COPD?

Background Patients with COPD have an increased risk of cardiovascular disease. Whilst pulmonary rehabilitation has proven benefit for exercise tolerance and quality of life, any effect on cardiovascular risk has not been fully investigated. We hypothesised that pulmonary rehabilitation, through the exercise and nutritional intervention, would address these factors. Methods Thirty-two stable patients with COPD commenced rehabilitation, and were compared with 20 age and gender matched controls at baseline assessment. In all subjects, aortic pulse wave velocity (PWV) an independent non-invasive predictor of cardiovascular risk, blood pressure (BP), interleukin-6 (IL-6) and fasting glucose and lipids were determined. These measures, and the incremental shuttle walk test (ISWT) were repeated in the patients who completed pulmonary rehabilitation. Results On commencement of rehabilitation aortic PWV was increased in patients compared with controls (p < 0.05), despite mean BP, age and gender being similar. The IL-6 was also increased (p < 0.05). Twenty-two patients completed study assessments. In these subjects, rehabilitation reduced mean (SD) aortic PWV (9.8 (3.0) to 9.3 (2.7) m/s (p < 0.05)), and systolic and diastolic BP by 10 mmHg and 5 mmHg respectively (p < 0.01). Total cholesterol and ISWT also improved (p < 0.05). On linear regression analysis, the reduction in aortic PWV was attributed to reducing the BP. Conclusion Cardiovascular risk factors including blood pressure and thereby aortic stiffness were improved following a course of standard multidisciplinary pulmonary rehabilitation in patients with COPD

An infinite genus mapping class group and stable cohomology

We exhibit a finitely generated group \M whose rational homology is isomorphic to the rational stable homology of the mapping class group. It is defined as a mapping class group associated to a surface \su of infinite genus, and contains all the pure mapping class groups of compact surfaces of genus $g$ with $n$ boundary components, for any $g\geq 0$ and $n>0$. We construct a representation of \M into the restricted symplectic group ${\rm Sp_{res}}({\cal H}_r)$ of the real Hilbert space generated by the homology classes of non-separating circles on \su, which generalizes the classical symplectic representation of the mapping class groups. Moreover, we show that the first universal Chern class in H^2(\M,\Z) is the pull-back of the Pressley-Segal class on the restricted linear group ${\rm GL_{res}}({\cal H})$ via the inclusion ${\rm Sp_{res}}({\cal H}_r)\subset {\rm GL_{res}}({\cal H})$.Comment: 14p., 8 figures, to appear in Commun.Math.Phy

Fredholm determinants and the statistics of charge transport

Using operator algebraic methods we show that the moment generating function of charge transport in a system with infinitely many non-interacting Fermions is given by a determinant of a certain operator in the one-particle Hilbert space. The formula is equivalent to a formula of Levitov and Lesovik in the finite dimensional case and may be viewed as its regularized form in general. Our result embodies two tenets often realized in mesoscopic physics, namely, that the transport properties are essentially independent of the length of the leads and of the depth of the Fermi sea.Comment: 30 pages, 2 figures, reference added, credit amende

Quantizing the damped harmonic oscillator

We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that unitary dilation of the contraction semigroup governing the dynamics of the system is a logical extension of the doubling procedure, and it allows one to avoid the mathematical difficulties encountered with the previous method.Comment: 4 pages, no figure

Functional Evolution of Free Quantum Fields

We consider the problem of evolving a quantum field between any two (in general, curved) Cauchy surfaces. Classically, this dynamical evolution is represented by a canonical transformation on the phase space for the field theory. We show that this canonical transformation cannot, in general, be unitarily implemented on the Fock space for free quantum fields on flat spacetimes of dimension greater than 2. We do this by considering time evolution of a free Klein-Gordon field on a flat spacetime (with toroidal Cauchy surfaces) starting from a flat initial surface and ending on a generic final surface. The associated Bogolubov transformation is computed; it does not correspond to a unitary transformation on the Fock space. This means that functional evolution of the quantum state as originally envisioned by Tomonaga, Schwinger, and Dirac is not a viable concept. Nevertheless, we demonstrate that functional evolution of the quantum state can be satisfactorily described using the formalism of algebraic quantum field theory. We discuss possible implications of our results for canonical quantum gravity.Comment: 21 pages, RevTeX, minor improvements in exposition, to appear in Classical and Quantum Gravit