Related papers: Numerical Techniques for the Study of Long-Time Co…
The analytic structure of elementary correlation functions of a quantum field is relevant for the calculation of masses of bound states and their time-like properties in general. In quantum chromodynamics, the calculation of correlation…
Already slightly eccentric orbits, such as those occupied by many old stars in the Galactic disk, are not well approximated by Lindblad's epicycle theory. Here, alternative approximations for flat orbits in axisymmetric stellar systems are…
Understanding natural relative motion trajectories is critical to enable fuel-efficient multi-satellite missions operating in complex environments. This paper studies the problem of computing and efficiently parameterizing satellite…
Correlation matrices contain a wide variety of spatio-temporal information about a dynamical system. Predicting correlation matrices from partial time series information of a few nodes characterizes the spatio-temporal dynamics of the…
In order to explore the effects of high levels of electron correlation on the real-time coupled cluster formalism and algorithmic behavior, we introduce a time-dependent implementation of the CC3 singles, doubles and approximate triples…
We give a method to determine relative periodic orbits in point vortex systems: it consists mainly into perform a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is…
Here we show how to determine the orbital parameters of a system composed of a star and N companions (that can be planets, brown-dwarfs or other stars), using a simple Fourier analysis of the radial velocity data of the star. This method…
Higher order correlation measurements involve multiple event averages which must run over unequal events to avoid statistical bias. We derive correction formulas for small event samples, where the bias is largest, and utilize the results to…
The four longest period Kuiper belt objects have orbital periods close to integer ratios with each other. A hypothetical planet with orbital period $\sim$17,117 years, semimajor axis $\sim$665 AU, would have N/1 and N/2 period ratios with…
We calculate spin correlation functions using IBM quantum processors, accessed online. We demonstrate the rotational invariance of the singlet state, interesting properties of the triplet states, and surprising features of a state of three…
We compute the equivariant fundamental class of the orbit closure of a linear series on the projective line. We also describe the boundary of the orbit closure and how the orbits specialise in one parameter families.
We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and…
High-volume feature-rich data sets are becoming the bread-and-butter of 21st century astronomy but present significant challenges to scientific discovery. In particular, identifying scientifically significant relationships between sets of…
It is widely known that numerically integrated orbits are more precise than analytical theories for celestial bodies. However, calculation of the positions of celestial bodies via numerical integration at time $t$ requires the amount of…
A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid excessive rounding error propagation of conventional…
This paper presents a novel formulation and solution of orbit determination over finite time horizons as a learning problem. We present an approach to orbit determination under very broad conditions that are satisfied for n-body problems.…
The Heisenberg scaling is typically associated with nonclassicality and entanglement. In this work, however, we discuss how classical long-range correlations between lattice sites in many-body systems may lead to a 1/N scaling in precision…
The existing periodic orbit theory of spectral correlations for classically chaotic systems relies on the Riemann-Siegel-like representation of the spectral determinants which is still largely hypothetical. We suggest a simpler derivation…
We propose a method to probe time dependent correlations of non trivial observables in many-body ultracold lattice gases. The scheme uses a quantum non-demolition matter-light interface, first, to map the observable of interest on the many…
The fixed-point theory and its applications to various areas of science are well known. In this paper we present some existence and uniqueness theorems for fixed circles of self-mappings on metric spaces with geometric interpretation. We…