Recent results, extending the Schmidt decomposition theorem to wavefunctions of pairs of identical particles, are reviewed. They are used to give a definition of reduced density operators in the case of two identical particles. Next, a method is discussed to calculate time averaged entanglement. It is applied to a pair of identical electrons in an otherwise empty band of the Hubbard model, and to a pair of bosons in the Bose-Hubbard model with infinite range hopping. The effect of degeneracy of the spectrum of the Hamiltonian on the average entanglement is emphasised.
A total solar eclipse occurred on 20 March 2015, with a totality path passing mostly above the North Atlantic Ocean, which resulted in a partial solar eclipse over Belgium and large parts of Europe. In anticipation of this event, a dedicated observational campaign was set up at the Belgian Solar-Terrestrial Centre of Excellence (STCE). The objective was to perform high-quality observations of the eclipse and the associated effects on the geospace environment by utilising the advanced space-and ground-based instrumentation available to the STCE in order to further our understanding of these effects, particularly on the ionosphere. The study highlights the crucial importance of taking into account the eclipse geometry when analysing the ionospheric behaviour during eclipses and interpreting the eclipse effects. A detailed review of the eclipse geometry proves that considering the actual obscuration level and solar zenith angle at ionospheric heights is much more important for the analysis than at the commonly referenced Earth's surface or at the plasmaspheric heights. The eclipse occurred during the recovery phase of a strong geomagnetic storm which certainly had an impact on (some of) the ionospheric characteristics and perhaps caused the omission of some ''low-profile'' effects. However, the analysis of the ionosonde measurements, carried out at unprecedented high rates during the eclipse, suggests the occurrence of travelling ionospheric disturbances (TIDs). Also, the high temporal and spatial resolution measurements proved very important in revealing and estimating some finer details of the delay in the ionospheric reaction and the ionospheric disturbances.
Traveling ionospheric disturbances (TIDs) are the ionospheric signatures of atmospheric gravity waves. Their identification and tracking is important because the TIDs affect all services that rely on predictable ionospheric radio wave propagation. Although various techniques have been proposed to measure TID characteristics, their real‐time implementation still has several difficulties. In this contribution, we present a new technique, based on the analysis of oblique Digisonde‐to‐Digisonde “skymap” observations, to directly identify TIDs and specify the TID wave parameters based on the measurement of angle of arrival, Doppler frequency, and time of flight of ionospherically reflected high‐frequency radio pulses. The technique has been implemented for the first time for the Network for TID Exploration project with data streaming from the network of European Digisonde DPS4D observatories. The performance is demonstrated during a period of moderate auroral activity, assessing its consistency with independent measurements such as data from auroral magnetometers and electron density perturbations from Digisondes and Global Navigation Satellite System stations. Given that the different types of measurements used for this assessment were not made at exactly the same time and location, and that there was insufficient coverage in the area between the atmospheric gravity wave sources and the measurement locations, we can only consider our interpretation as plausible and indicative for the reliability of the extracted TID characteristics. In the framework of the new TechTIDE project (European Commission H2020), a retrospective analysis of the Network for TID Exploration results in comparison with those extracted from Global Navigation Satellite System total electron content‐based methodologies is currently being attempted, and the results will be the objective of a follow‐up paper.
A reliable interpretation of solar eclipse effects on the geospace environment, and on the ionosphere in particular, necessitates a careful consideration of the so‐called eclipse geometry. A solar eclipse is a relatively rare astronomical phenomenon, which geometry is rather complex, specific for each event, and fast changing in time. The standard, most popular way to look at the eclipse geometry is via the two‐dimensional representation (map) of the solar obscuration on the Earth's surface, in which the path of eclipse totality is drawn together with isolines of the gradually‐decreasing eclipse magnitude farther away from this path. Such “surface maps” are widely used to readily explain some of the solar eclipse effects including, for example, the well‐known decrease in total ionization (due to the substantial decrease in solar irradiation), usually presented by the popular and easy to understand ionospheric characteristic of total electron content (TEC). However, many other effects, especially those taking place at higher altitudes, cannot be explained in this fashion. Instead, a more detailed description of the umbra (and penumbra), would be required. This paper addresses the issue of eclipse geometry effects on various ionospheric observations carried out during the total solar eclipse of 21 August 2017. In particular, GPS‐based TEC measurements were analyzed and eclipse effects on the ionosphere are interpreted with respect to the actual eclipse geometry at ionospheric heights. Whenever possible, a comparison was made with results from other eclipse events.
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