Related papers: An Accessible Formulation for Defining the SI Seco…

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 $t$…

Fundamentally, every static program analyser searches for a proof through a combination of heuristics providing candidate solutions and a candidate validation technique. Essentially, the heuristic reduces a second-order problem to a…

$^{133}$Cs, which is the only stable cesium (Cs) isotope, is one of the most investigated elements in atomic spectroscopy and was used to realize the atomic clock in 1955. Among all atomic clocks, the cesium atomic clock has a special…

Optical lattice clocks with uncertainty and instability in the $10^{-17}$-range and below have so far been demonstrated exclusively using fermions. Here, we demonstrate a bosonic optical lattice clock with $3\times 10^{-18}$ instability and…

We performed accurate calculation of $\alpha$-dependence ($\alpha=e^2/hc$) of the transition frequencies for ions, which are used in a search for the variation of the fine structure constant $\alpha$ in space-time. We use Dirac-Hartree-Fock…

Atomic clocks have been transformational in science and technology, leading to innovations such as global positioning, advanced communications, and tests of fundamental constant variation. Next-generation optical atomic clocks can extend…

This study presents a novel optimisation technique for atomic structure calculations using the Flexible Atomic Code, focussing on complex multielectron systems relevant to $r$-process nucleosynthesis and kilonova modelling. We introduce a…

The presence of second-order smoothness for objective functions of optimization problems can provide valuable information about their stability properties and help us design efficient numerical algorithms for solving these problems. Such…

The revised International System of Units (SI), expected to be approved late in 2018, has implications for physics pedagogy; the ampere definition which dates from 1948 will be replaced by a definition that fixes the numerical value of the…

The transfer of high-quality time-frequency signals between remote locations underpins a broad range of applications including precision navigation and timing, the new field of clock-based geodesy, long-baseline interferometry, coherent…

Sub-picosecond timing synchronization can enable future optical timekeeping networks, including coherent phased array radar imaging at GHz levels, intercontinental clock comparisons for the redefinition of the second, chronometric leveling,…

Fiore and Hur recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a…

Plans are underway to redefine the International System of Units (SI) around 2018. The New SI specifies the values of certain physical constants to define units. This article explains the New SI in a way that could be used to present it to…

Demands from several areas of science and technology have lead to a worldwide search for accurate optical clocks with an uncertainty of 1 part in $10^{18}$, which is $10^{3}$ times more accurate than the present day cesium atomic clocks…

We propose a new approach to compute an interval over-approximation of the finite time reachable set for a large class of nonlinear systems. This approach relies on the notions of sensitivity matrices, which are the partial derivatives…

Some classic second-order sufficient optimality conditions in the calculus of variations are shown to be equivalent, while also introducing a new equivalent second-order condition which is extremely easy to apply: simply integrate a linear…

We perform calculations of electronic structure of Cm$^{15+}$ and Bk$^{16+}$ ions and demonstrate that they have transitions which combine the features of atomic optical clocks with the enhanced sensitivity to the variations of the fine…

Thanks to common-mode noise rejection, differential configurations are crucial for realistic applications of phase and frequency estimation with atom interferometers. Currently, differential protocols with uncorrelated particles and…

It is shown that the dynamic differential scalar polarisability of the $S_{1/2}-D_{5/2}$ transition in $^{138}$Ba$^+$ can be determined to an inaccuracy below $0.5\%$ across a wide wavelength range ($\lambda>700\,\mathrm{nm}$). This can be…

This paper introduces a new notion of quantum recursion of which the control flow of the computation is quantum rather than classical as in the notions of recursion considered in the previous studies of quantum programming. A typical…