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The possibility of detecting the gravitomagnetic clock effect using artificial Earth satellites provides the incentive to develop a more intuitive approach to its derivation. We first consider two test electric charges moving on the same…
We extend the mathematical model based on stochastic differential equations describing the error gained by an atomic clock to the cases of anomalous behavior including jumps and an increase of instability. We prove an exact iterative…
Clock synchronization between the ground and satellites is a fundamental issue in future quantum telecommunication, navigation, and global positioning systems. Here, we propose a scheme of near-Earth orbit satellite-based quantum clock…
The recent article `Satellite conjunction analysis and the false confidence theorem' (Balch, Martin, and Ferson, 2019, Proceedings of the Royal Society, Series A) points to certain difficulties with Bayesian analysis when used for models…
We derive the analytical expression of the coordinate time $t$ in terms of the eccentric anomaly $u$ at the second post-Newtonian order in General Relativity for a compact binary system moving on eccentric orbits. The parametrization of $t$…
Perhaps the most significant drawback, which the Copenhagen interpretation (still the most popular interpretation of quantum theory) suffers from, is the classical-quantum divide between the large classical systems that carry out…
Solutions to scalar theories with derivative self-couplings often have regions where non-linearities are important. Given a classical source, there is usually a region, demarcated by the Vainshtein radius, inside of which the classical…
Satellite conjunction analysis is the assessment of collision risk during a close encounter between a satellite and another object in orbit. A counterintuitive phenomenon has emerged in the conjunction analysis literature, namely,…
Theoretical analyses of stochastic search algorithms, albeit few, have always existed since these algorithms became popular. Starting in the nineties a systematic approach to analyse the performance of stochastic search heuristics has been…
A technique called analytic perturbation theory, which respects the required analytic properties, consistent with causality, is applied to the definition of the running coupling in the timelike region, to the description of inclusive…
The Slater-type orbital basis with non-integer principal quantum numbers is a physically and mathematically motivated choice for molecular electronic structure calculations in both non-relativistic and relativistic theory. The…
The canonical formalism of general relativity affords a particularly interesting characterisation of the infamous hole argument. It also provides a natural formalism in which to relate the hole argument to the problem of time in classical…
We study the correlation of orbital poles of the 11 classical satellite galaxies of the Milky Way, comparing results from previous proper motions with the independent data by Gaia DR2. Previous results on the degree of correlation and its…
Artificial intelligence is rapidly transforming astronomical research, yet the scientific community has largely treated this transformation as an engineering challenge rather than an epistemological one. This perspective article argues that…
Calculating the long term solution of ordinary differential equations, such as those of the $N$-body problem, is central to understanding a wide range of dynamics in astrophysics, from galaxy formation to planetary chaos. Because generally…
The notions of time in the theories of Newton and Einstein are reviewed so that certain of their assumptions are clarified. These assumptions will be seen as the causes of the incompatibility between the two different ways of understanding…
In a major advance and simplification of this field, we show that A Local Resolution of the Problem of Time - also viewable as A Local Theory of Background Independence - can at the classical level be described solely by of Lie's…
The new combined formulas have been established for the complex and real rotation-angular functions arising in the evaluation of two-center overlap integrals over arbitrary atomic orbitals in molecular coordinate system. These formulas can…
Counterfactual thinking is a crucial yet challenging topic for artificial intelligence to learn knowledge from data and ultimately improve performance for new scenarios. Many research works, including the Potential Outcome Model (POM) and…
We introduce three representative topics in semi-classical analysis. Starting from the correspondence between classical and quantum mechanics, basic semi-classical analysis tools and results are presented. The three topics are investigated…