Symplectically Covariant Schr\"{o}dinger Equation in Phase Space

A classical theorem of Stone and von Neumann says that the Schr\"{o}dinger representation is, up to unitary equivalences, the only irreducible representation of the Heisenberg group on the Hilbert space of square-integrable functions on configuration space. Using the Wigner-Moyal transform we construct an irreducible representation of the Heisenberg group on a certain Hilbert space of square-integrable functions defined on phase space. This allows us to extend the usual Weyl calculus into a phase-space calculus and leads us to a quantum mechanics in phase space, equivalent to standard quantum mechanics. We also briefly discuss the extension of metaplectic operators to phase space and the probabilistic interpretation of the solutions of the phase space Schr\"{o}dinger equationComment: To appear in J Phys

Quantum Blobs

Quantum blobs are the smallest phase space units of phase space compatible with the uncertainty principle of quantum mechanics and having the symplectic group as group of symmetries. Quantum blobs are in a bijective correspondence with the squeezed coherent states from standard quantum mechanics, of which they are a phase space picture. This allows us to propose a substitute for phase space in quantum mechanics. We study the relationship between quantum blobs with a certain class of level sets defined by Fermi for the purpose of representing geometrically quantum states.Comment: Prepublication. Dedicated to Basil Hile

The "Symplectic Camel Principle" and Semiclassical Mechanics

Gromov's nonsqueezing theorem, aka the property of the symplectic camel, leads to a very simple semiclassical quantiuzation scheme by imposing that the only "physically admissible" semiclassical phase space states are those whose symplectic capacity (in a sense to be precised) is nh + (1/2)h where h is Planck's constant. We the construct semiclassical waveforms on Lagrangian submanifolds using the properties of the Leray-Maslov index, which allows us to define the argument of the square root of a de Rham form.Comment: no figures. to appear in J. Phys. Math A. (2002

Weather conditions and daily television use in the Netherlands, 1996–2005

This study examines the impact of daily atmospheric weather conditions on daily television use in the Netherlands for the period 1996–2005. The effects of the weather parameters are considered in the context of mood and mood management theory. It is proposed that inclement and uncomfortable weather conditions are associated with lower human mood, and that watching entertainment and avoiding informational programs may serve to repair such mood. We consequently hypothesize that people spend more time watching television if inclement and uncomfortable weather conditions (low temperatures, little sunshine, much precipitation, high wind velocity, less daylight) coincide with more airtime for entertainment programs, but that they view less if the same weather conditions coincide with more airtime devoted to information fare. We put this interaction thesis to a test using a time series analysis of daily television viewing data of the Dutch audience obtained from telemeters (T = 3,653), merged with meteorological weather station statistics and program broadcast figures, whilst controlling for a wide array of recurrent and one-time societal events. The results provide substantial support for the proposed interaction of program airtime and the weather parameters temperature and sunshine on aggregate television viewing time. Implications of the findings are discussed

Induction of labour versus expectant management in women with preterm prelabour rupture of membranes between 34 and 37 weeks (the PPROMEXIL-trial)

Contains fulltext : 53155.pdf ( ) (Open Access)BACKGROUND: Preterm prelabour rupture of the membranes (PPROM) is an important clinical problem and a dilemma for the gynaecologist. On the one hand, awaiting spontaneous labour increases the probability of infectious disease for both mother and child, whereas on the other hand induction of labour leads to preterm birth with an increase in neonatal morbidity (e.g., respiratory distress syndrome (RDS)) and a possible rise in the number of instrumental deliveries. METHODS/DESIGN: We aim to determine the effectiveness and cost-effectiveness of immediate delivery after PPROM in near term gestation compared to expectant management. Pregnant women with preterm prelabour rupture of the membranes at a gestational age from 34+0 weeks until 37+0 weeks will be included in a multicentre prospective randomised controlled trial. We will compare early delivery with expectant monitoring.The primary outcome of this study is neonatal sepsis. Secondary outcome measures are maternal morbidity (chorioamnionitis, puerperal sepsis) and neonatal disease, instrumental delivery rate, maternal quality of life, maternal preferences and costs. We anticipate that a reduction of neonatal infection from 7.5% to 2.5% after induction will outweigh an increase in RDS and additional costs due to admission of the child due to prematurity. Under these assumptions, we aim to randomly allocate 520 women to two groups of 260 women each. Analysis will be by intention to treat. Additionally a cost-effectiveness analysis will be performed to evaluate if the cost related to early delivery will outweigh those of expectant management. Long term outcomes will be evaluated using modelling. DISCUSSION: This trial will provide evidence as to whether induction of labour after preterm prelabour rupture of membranes is an effective and cost-effective strategy to reduce the risk of neonatal sepsis. CONTROLLED CLINICAL TRIAL REGISTER: ISRCTN29313500

Central Anomaly Magnetization High documentation of crustal accretion along the East Pacific Rise (9°55′–9°25′N)

Author Posting. © American Geophysical Union, 2008. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry Geophysics Geosystems 9 (2008): Q04015, doi:10.1029/2007GC001611.Near-bottom magnetic data collected along the crest of the East Pacific Rise between 9°55′ and 9°25′N identify the Central Anomaly Magnetization High (CAMH), a geomagnetic anomaly modulated by crustal accretionary processes over timescales of ∼104 years. A significant decrease in CAMH amplitude is observed along-axis from north to south, with the steepest gradient between 9°42′ and 9°36′N. The source of this variation is neither a systematic change in geochemistry nor varying paleointensity at the time of lava eruption. Instead, magnetic moment models show that it can be accounted for by an observed ∼50% decrease in seismic Layer 2A thickness along-axis. Layer 2A is assumed to be the extrusive volcanic layer, and we propose that this composes most of the magnetic source layer along the ridge axis. The 9°37′N overlapping spreading center (OSC) is located at the southern end of the steep CAMH gradient, and the 9°42′–9°36′N ridge segment is interpreted to be a transition zone in crustal accretion processes, with robust magmatism north of 9°42′N and relatively low magmatism at present south of 9°36′N. The 9°37′N OSC is also the only bathymetric discontinuity associated with a shift in the CAMH peak, which deviates ∼0.7 km to the west of the axial summit trough, indicating southward migration of the OSC. CAMH boundaries (defined from the maximum gradients) lie within or overlie the neovolcanic zone (NVZ) boundaries throughout our survey area, implying a systematic relationship between recent volcanic activity and CAMH source. Maximum flow distances and minimum lava dip angles are inferred on the basis of the lateral distance between the NVZ and CAMH boundaries. Lava dip angles average ∼14° toward the ridge axis, which agrees well with previous observations and offers a new method for estimating lava dip angles along fast spreading ridges where volcanic sequences are not exposed.The research project was funded by National Science Foundation under grants OCE-9819261 and OCE- 0096468