Tensor network methods have become a powerful class of tools to capture strongly correlated matter, but methods to capture the experimentally ubiquitous family of models at finite temperature beyond ...one spatial dimension are largely lacking. We introduce a tensor network algorithm able to simulate thermal states of two-dimensional quantum lattice systems in the thermodynamic limit. The method develops instances of projected entangled pair states and projected entangled pair operators for this purpose. It is the key feature of this algorithm to resemble the cooling down of the system from an infinite temperature state until it reaches the desired finite-temperature regime. As a benchmark, we study the finite-temperature phase transition of the Ising model on an infinite square lattice, for which we obtain remarkable agreement with the exact solution. We then turn to study the finite-temperature Bose-Hubbard model in the limits of two (hard-core) and three bosonic modes per site. Our technique can be used to support the experimental study of actual effectively two-dimensional materials in the laboratory, as well as to benchmark optical lattice quantum simulators with ultracold atoms.
We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the projected entangled-pair state algorithm for finite lattice systems ...F. Verstraete and J. I. Cirac, arxiv:cond-mat/0407066 and the infinite time-evolving block decimation algorithm for infinite one-dimensional lattice systems G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)10.1103/PhysRevLett.98.070201. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analyzing its second order quantum phase transition.
The International GNSS Service (IGS) Working Group on Ionosphere was created in 1998. Since then, the Scientific community behind IGS, in particular CODE, ESA, JPL and UPC, have been continuosly ...contributing to reliable IGS combined vertical total electron content (VTEC) maps in both rapid and final schedules. The details on how these products are being generated, performance numbers, proposed improvement as far as VTEC evolution trends during near one Solar Cycle, are summarized in this paper. The confirmation of (1) the good performance of the IGS combined VTEC maps, and (2) the characteristic VTEC variability periods, are two main results of this work.
This work reviews an ionospheric activity indicator useful for identifying disturbed periods affecting the performance of Global Navigation Satellite System (GNSS). This index is based in the Along ...Arc TEC Rate (AATR) and can be easily computed from dual-frequency GNSS measurements. The AATR indicator has been assessed over more than one Solar Cycle (2002–2017) involving about 140 receivers distributed world-wide. Results show that it is well correlated with the ionospheric activity and, unlike other global indicators linked to the geomagnetic activity (i.e.
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ST
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), it is sensitive to the regional behaviour of the ionosphere and identifies specific effects on GNSS users. Moreover, from a devoted analysis of different Satellite Based Augmentation System (SBAS) performances in different ionospheric conditions, it follows that the AATR indicator is a very suitable mean to reveal whether SBAS service availability anomalies are linked to the ionosphere. On this account, the AATR indicator has been selected as the metric to characterise the ionosphere operational conditions in the frame of the European Space Agency activities on the European Geostationary Navigation Overlay System (EGNOS). The AATR index has been adopted as a standard tool by the International Civil Aviation Organization (ICAO) for joint ionospheric studies in SBAS. In this work we explain how the AATR is computed, paying special attention to the cycle-slip detection, which is one of the key issues in the AATR computation, not fully addressed in other indicators such as the Rate Of change of the TEC Index (ROTI). After this explanation we present some of the main conclusions about the ionospheric activity that can extracted from the AATR values during the above mentioned long-term study. These conclusions are: (a) the different spatial correlation related with the MOdified DIP (MODIP) which allows to clearly separate high, mid and low latitude regions, (b) the large spatial correlation in mid latitude regions which allows to define a planetary index, similar to the geomagnetic ones, (c) the seasonal dependency which is related with the longitude and (d) the variation of the AATR value at different time scales (hourly, daily, seasonal, among others) which confirms most of the well-known time dependences of the ionospheric events, and finally, (e) the relationship with the space weather events.
The solar cycle 24 will not be registered as the most intense of the last cycles. In fact, its intensity is roughly half of the previous cycle and the ionospheric effects experienced in this cycle ...have been far milder than originally expected, despite having several major ionospheric storms in this period, as the so‐called St. Patrick's Day's ionospheric storm. On the other hand, in this same period of time, the Galileo system has started the deployment phase and it started the In‐Orbit‐Validation campaign on 2013 with the first four full operational satellites, following the launch of a number of additional satellites allowing the declaration of Initial Services in December 2016 and targeting the Full Operational Capability by 2020. Thus, during this period of time, Galileo has been broadcasting the 3 Az coefficients needed to use the NeQuick G for correcting the ionospheric delay for single‐frequency users. In this work, the full analysis of the performance of the NeQuick G for the last solar cycle will be presented along with the detailed analysis of some of the most relevant ionospheric storms occurred during the very same period. In general, the NeQuick G presents around 50 cm better root mean square than the Global Positioning System broadcast model for all the period of study. As an internal measure of the goodness of the NeQuick G, the percentage of slant total electron content inside of target Galileo specification will also be analyzed.
Plain Language Summary
Galileo constellation is deploying, and at the current state, first tests can be done to monitor the quality of the signal and broadcast parameters. One of the most important broadcast parameters for mass market users are the ones related with the NeQuick G, the algorithm that allows you to correct the signal from ionosphere errors. In this paper, a study of the performance of the NeQuick G is presented and compared to the Global Positioning System one. Moreover, the performance of the navigation solution with Galileo, with the current reduced number of satellites, is compared to the Global Positioning System one.
Key Points
Performance of Galileo single‐frequency model since March 2013 till December 2016 is shown
Comparison of performances for different ionospheric models is done. In general, Galileo single‐frequency model shows better performance than GPS model
Positioning results performed with stand‐alone Galileo demonstrate that the Initial Open Service performance targets for Galileo Initial Services are met
In this paper, different aspects of the application of the second‐order ionospheric term (abbreviated as I2) and its impact on geodetic estimates are studied. A method to correct the GPS observations ...from this effect is proposed. This method provides a more accurate correction to the GPS measurements (in some cases, it can even be 50% better) with respect to other ways of computing such effect. Moreover, this method can be applied routinely to estimate geodetic parameters. Applying the I2 correction to subdaily differential positioning, several relationships between the deviation of the parameter estimates and the I2 term are derived in the context of a new global approach to the problem. In particular, it is shown that the effect in receiver position mainly depends on the differential value of this term between GPS receivers, while the satellite clocks are directly affected by the undifferenced values. Data from the International GNSS Service (IGS) global network of receivers have been gathered over a period of 21 months. These data have been used to study the I2 effect on the geodetic estimates, such as receiver positions, satellite clocks, and orbits. The most important effect appears for the satellite clocks, and it can be greater than 1 cm depending on the geographical location, comparable to the IGS nominal accuracies. The effect on orbits consists of a global contribution of several millimeters (which confirms the geocenter displacement detected by other authors) plus a subdaily contribution, also of several millimeters, that is geographically dependent, also comparable to the IGS nominal accuracies. As for the position of receivers, the obtained shifts are, in general, at submillimeter level and are directed southward for low‐latitude receivers and northward for high‐latitude receivers. These results will be explained in detail since they are not completely in agreement with the ones presented in previous works.
High precision Global Navigation Satellite Systems (GNSS) positioning and time transfer require correcting signal delays, in particular higher‐order ionospheric (I2+) terms. We present a consolidated ...model to correct second‐ and third‐order terms, geometric bending and differential STEC bending effects in GNSS data. The model has been implemented in an online service correcting observations from submitted RINEX files for I2+ effects. We performed GNSS data processing with and without including I2+ corrections, in order to investigate the impact of I2+ corrections on GNSS products. We selected three time periods representing different ionospheric conditions. We used GPS and GLONASS observations from a global network and two regional networks in Poland and Brazil. We estimated satellite orbits, satellite clock corrections, Earth rotation parameters, troposphere delays, horizontal gradients, and receiver positions using global GNSS solution, Real‐Time Kinematic (RTK), and Precise Point Positioning (PPP) techniques. The satellite‐related products captured most of the impact of I2+ corrections, with the magnitude up to 2 cm for clock corrections, 1 cm for the along‐ and cross‐track orbit components, and below 5 mm for the radial component. The impact of I2+ on troposphere products turned out to be insignificant in general. I2+ corrections had limited influence on the performance of ambiguity resolution and the reliability of RTK positioning. Finally, we found that I2+ corrections caused a systematic shift in the coordinate domain that was time‐ and region‐dependent and reached up to −11 mm for the north component of the Brazilian stations during the most active ionospheric conditions.
Key Points
We present a consolidated model to correct GNSS data for higher‐order ionospheric corrections
We have implemented the model in an online service correcting RINEX files
We investigated the impact of the delays on satellite orbits and clocks, troposphere delay and gradients, RTK, and PPP positioning
The ESA MONITOR network is composed of high-frequency-sampling global navigation satellite systems (GNSS) receivers deployed mainly at low and high latitudes to study ionosphere variability and ...jointly with global GNSS data and ionospheric processing software in support of the GNSS and its satellite-based augmentation systems (SBAS) like the European EGNOS. In a recent phase of the project, the network was merged with the CNES/ASECNA network and new receivers were added to complement the latter in the western African sector. This paper summarizes MONITOR, presenting two case studies on scintillations (using almost 2 years of data measurements). The first case occurred during the major St. Patrick's Day geomagnetic storm in 2015. The second case study was performed in the last phase of the project, which was supported by ESA EGNOS Project Office, when we paid special attention to extreme events that might degrade the system performance of the European EGNOS.
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