The characterization of the ionosphere and its impact on the propagation of radio-wave signals has received an increasing interest for satellite communications, Global Navigation Satellite Systems ...(GNSS) applications (i.e. navigation and timing), and Earth Observation (EO) missions, especially low frequency SAR missions and GNSS-Reflectometry (GNSS-R). Although the main climatological models for the mean stable part of the electron density in the ionospheric layers (e.g. IRI or NeQuick) or for the magnetic field (e.g. WMM) have been significantly improved in the past years, the inhomogeneous part, responsible for scintillation effects, can still be significantly improved, since models are based on relatively old data (e.g. WBMOD), or the climatological inputs are limited to properly characterize all latitudes and solar conditions (e.g. GISM or WAM). ESA's CLIM IONO study aims to use the experimental observations of the ionosphere collected in the past years to assess the performance of climatological ionosphere models, with the focus on scintillation models, in order to evaluate their ability to properly support future needs, to identify weak areas if any, to propose recommendations for improvements and to implement these improvements whenever possible in existing models. This work focuses on the capabilities of GNSS-R techniques to characterize ionospheric scintillation, notably at low and high latitudes.
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 ultra-cold atoms.
Continuous unitary transformations are a powerful tool to extract valuable information out of quantum many-body Hamiltonians, in which the so-called flow equation transforms the Hamiltonian to a ...diagonal or block-diagonal form in second quantization. Yet, one of their main challenges is how to approximate the infinitely-many coupled differential equations that are produced throughout this flow. Here we show that tensor networks offer a natural and non-perturbative truncation scheme in terms of entanglement. The corresponding scheme is called "entanglement-CUT" or eCUT. It can be used to extract the low-energy physics of quantum many-body Hamiltonians, including quasiparticle energy gaps. We provide the general idea behind eCUT and explain its implementation for finite 1d systems using the formalism of matrix product operators. We also present proof-of-principle results for the spin-1/2 1d quantum Ising model and the 3-state quantum Potts model in a transverse field. Entanglement-CUTs can also be generalized to higher dimensions and to the thermodynamic limit.
A generic software tool to evaluate the impact of ionospheric disturbances is presented, including low and high latitude physically-based models, and low and high frequency fluctuations. This tool ...has been developed specifically to assess the performance of navigation receivers, but it is ready to simulate other frequencies and even receivers in dynamic conditions, which allows it to be used in other applications such as communications, GNSS-R, radar altimetry or SAR.
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