Related papers: A mathematical model for the atomic clock error in…
We establish an integration by parts formula based on jumps times in an abstract framework in order to study the regularity of the law for processes solution of stochastic differential equations with jumps.
We consider some implications of the mass defect on the frequency of atomic transitions. We have found that some well-known frequency shifts (gravitational shift and motion-induced shifts such as: quadratic Doppler and micromotion shifts)…
This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational…
It is shown how possible corrections to ordinary quantum mechanics described by the Lindblad equation might be detected by exploiting the great precision of atomic clocks.
Stochastic systems with memory naturally appear in life science, economy, and finance. We take the modelling point of view of stochastic functional delay equations and we study these structures when the driving noises admit jumps. Our…
Time estimation is a fundamental task that underpins precision measurement, global navigation systems, financial markets, and the organisation of everyday life. Many biological processes also depend on time estimation by nanoscale clocks,…
This study introduces new time-stepping strategies with built-in global error estimators. The new methods propagate the defect along with the numerical solution much like solving for the correction or Zadunaisky's procedure; however, the…
This guide offers suggestions/insights on uncertainty quantification of nuclear structure models. We discuss a simple approach to statistical error estimates, strategies to assess systematic errors, and show how to uncover…
The use of stochastic models, in effect piecewise deterministic Markov processes (PDMP), has become increasingly popular especially for the modeling of chemical reactions and cell biophysics. Yet, exact simulation methods, for the…
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…
Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…
In standard quantum theory, time is not an observable. It enters as a parameter in the Schr\"odinger equation, but there is no measurement operator associated to it. Nevertheless, one may take an operational viewpoint and regard time as the…
We review experimental progress on optical atomic clocks and frequency transfer, and consider the prospects of using these technologies for geodetic measurements. Today, optical atomic frequency standards have reached relative frequency…
We develop an abstract model of atomic clocks that fully describes the dynamics of repeated synchronization between a classical oscillator and a quantum reference. We prove existence of a stationary state of the model and study its…
The paper addresses the critical problem of identifying unknown parameters of an atomic clock ensemble. The ensemble model is considered as a set of individual clock models, where each clock is described by a second-order linear stochastic…
An analytical method for investigation of the evolution of dynamical systems {\it with independent on time accuracy} is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application…
The dynamics of an unique type of clock mechanism known as grasshopper escapement is investigated with the aim of evaluating its accuracy in a noisy environment. It is demonstrated that the clock's precision scales linearly with the rate of…
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…
A key feature of the classical Fluctuation Dissipation theorem is its ability to approximate the average response of a dynamical system to a sufficiently small external perturbation from an appropriate time correlation function of the…
Atomic clock technology is advancing rapidly, now reaching stabilities of $\Delta f/f \sim 10^{-18}$, which corresponds to resolving $1$ cm in equivalent geoid height over an integration timescale of about 7 hours. At this level of…