The quantum state vector in phase space and Gabor's windowed Fourier transform

Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in the state vector and anti-linear in a fixed `window state vector'. Here aspects of this construction are explored, with emphasis on the connection with Gabor's `windowed Fourier transform'. The amplitudes that arise for simple quantum states from various choices of window are presented as illustrations. Generalized Bargmann representations of the state vector appear as special cases, associated with Gaussian windows. For every choice of window, amplitudes lie in a corresponding linear subspace of square-integrable functions on phase space. A generalized Born interpretation of amplitudes is described, with both the Wigner function and a generalized Husimi function appearing as quantities linear in an amplitude and anti-linear in its complex conjugate. Schr\"odinger's time-dependent and time-independent equations are represented on phase space amplitudes, and their solutions described in simple cases.Comment: 36 pages, 6 figures. Revised in light of referees' comments, and further references adde

Stress avulsion of the tibial tuberosity after tension band wiring of a patellar fracture: a case report

INTRODUCTION: To the best of our knowledge there is no other report of an elderly patient who was surgically treated for a patellar fracture with tension band wiring and who subsequently suffered from an avulsion fracture of the tibial tuberosity. The combination of a patellar fracture and avulsion of the patellar ligament has only been described as complication after bone-patellar tendon-bone anterior cruciate ligament reconstructions. However, due to demographic changes and more elderly patients treated this injury may become more frequent in future. CASE PRESENTATION: We present the case of an 81 year old female who sustained an oblique patellar fracture after a direct contact injury of the left knee when falling on ice. Consequently the patellar fracture was openly reduced and stabilized with tension band wiring. The follow-up was uneventful till three months after surgery when the patient noticed a spontaneous avulsion fracture of the tibial tuberosity (Ogden type 3). The tibial tuberosity fragment was reattached with two non-resorbable sutures looped around two modified AO cortical 3.5 mm long neck screws. Intraoperatively multiple bone cysts were seen. Biopsies were not taken to prevent further fragmentation of the tibial tuberosity. The patient was followed up with anteroposterior and lateral full weight bearing radiographs and clinical assessment at 6, 12 weeks and 6 months after surgery. Recovery was completely pain free with full satisfaction. CONCLUSION: In conclusion in elderly patients with a patella fracture a possible associated but not obvious fracture of the tibial tuberosity should be ruled out and the postoperative rehabilitation protocol after tension band wiring of the patella might have to be individually adjusted to bone quality and course of the fracture

Homogeneously derived transit timings for 17 exoplanets and reassessed TTV trends for WASP-12 and WASP-4

We homogeneously analyse ∼3.2 × 105 photometric measurements for ∼1100 transit lightcurves belonging to 17 exoplanet hosts. The photometric data cover 16 years 2004–2019 and include amateur and professional observations. Old archival lightcurves were reprocessed using up-to-date exoplanetary parameters and empirically debiased limb-darkening models. We also derive self-consistent transit and radial-velocity fits for 13 targets. We confirm the nonlinear TTV trend in the WASP-12 data at a high significance, and with a consistent magnitude. However, Doppler data reveal hints of a radial acceleration about ( − 7.5 ± 2.2) m/s/yr, indicating the presence of unseen distant companions, and suggesting that roughly 10 per cent of the observed TTV was induced via the light-travel (or Roemer) effect. For WASP-4, a similar TTV trend suspected after the recent TESS observations appears controversial and model-dependent. It is not supported by our homogeneus TTV sample, including 10 ground-based EXPANSION lightcurves obtained in 2018 simultaneously with TESS. Even if the TTV trend itself does exist in WASP-4, its magnitude and tidal nature are uncertain. Doppler data cannot entirely rule out the Roemer effect induced by possible distant companions

Utilizing a Global Network of Telescopes to Update the Ephemeris for the Highly Eccentric Planet HD 80606 b and to Ensure the Efficient Scheduling of JWST

The transiting planet HD 80606 b undergoes a 1000 fold increase in insolation during its 111 days orbit due to it being highly eccentric (e = 0.93). The planet's effective temperature increases from 400 to over 1400 K in a few hours as it makes a rapid passage to within 0.03 au of its host star during periapsis. Spectroscopic observations during the eclipse (which is conveniently oriented a few hours before periapsis) of HD 80606 b with the James Webb Space Telescope (JWST) are poised to exploit this highly variable environment to study a wide variety of atmospheric properties, including composition, chemical and dynamical timescales, and large scale atmospheric motions. Critical to planning and interpreting these observations is an accurate knowledge of the planet's orbit. We report on observations of two full-transit events: 2020 February 7 as observed by the TESS spacecraft and 2021 December 7-8 as observed with a worldwide network of small telescopes. We also report new radial velocity observations which, when analyzed with a coupled model to the transits, greatly improves the planet's orbital ephemeris. Our new orbit solution reduces the uncertainty in the transit and eclipse timing of the JWST era from tens of minutes to a few minutes. When combined with the planned JWST observations, this new precision may be adequate to look for non-Keplerian effects in the orbit of HD 80606 b

Ultraviolet radiation effects on fruit surface respiration and chlorophyll fluorescence

High-value fruit crops are exposed to a range of environmental conditions that can reduce fruit quality. Solar injury (SI) or sunburn is a common disorder in tropical, sub-tropical, and temperate climates and is related to: 1) high fruit surface temperature; 2) high visible light intensity; and, 3) ultraviolet radiation (UV). Positional changes in fruit that are caused by increased weight or abrupt changes that result from summer pruning, limb breakage, or other damage to the canopy can expose fruit to high solar radiation levels, increased fruit surface temperatures, and increased UV exposure that are higher than the conditions to which they are adapted. In our studies, we examined the effects of high fruit surface temperature, saturating photosynthetically-active radiation (PAR), and short-term UV exposure on chlorophyll fluorescence, respiration, and photosynthesis of fruit peel tissues from tropical and temperate fruit in a simulation of these acute environmental changes. All tropical fruits (citrus, macadamia, avocado, pineapple, and custard apple) and the apple cultivars 'Gala', 'Gold Rush', and 'Granny Smith' increased dark respiration (A0) when exposed to UV, suggesting that UV repair mechanisms were induced. The maximum quantum efficiency of photosystem II (Fv/Fm) and the quantum efficiency of photosystem II (ΦII) were unaffected, indicating no adverse effects on photosystem II (PSII). In contrast, 'Braeburn' apple had a reduced Fv/Fm with no increase in A0 on all sampling dates. There was a consistent pattern in all studies. When Fv/Fm was unaffected by UV treatment, A0 increased significantly. Conversely, when Fv/Fm was reduced by UV treatment, then A0 was unaffected. The pattern suggests that when UV repair mechanisms are effective, PSII is adequately protected, and that this protection occurs at the cost of higher respiration. However, when the UV repair mechanisms are ineffective, not only is PSII damaged, but there is additional short-term damage to the repair mechanisms, indicated by a lack of respiration to provide energy

Sistema de plantio direto - recomendações técnicas.

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