Related papers: Finding how many isolating integrals of motion an …
The transition between ballistic and diffusive motion poses difficult problems in several fields of physics. In this work we show how to calculate the spectra of the correlation functions between fields of arbitrary spatial dependence as…
The minimum orbital intersection distance is used as a measure to assess potential close approaches and collision risks between astronomical objects. Methods to calculate this quantity have been proposed in several previous publications.…
The account of electron correlation and its efficient separation into dynamic and nondynamic parts plays a key role in the development of computational methods. In this paper we suggest a physically-sound matrix formulation to split…
Loop calculations involve the evaluation of divergent integrals. Usually [1] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers…
We present a new procedure to identify observations of known objects in large data sets of unlinked detections. It begins with a Keplerian integrals method that allows us to link two tracklets, computing preliminary orbits, even when the…
The correlation functions related to topological phase transitions in inversion-symmetric lattice models described by $2\times 2$ Dirac Hamiltonians are discussed. In one dimension, the correlation function measures the charge-polarization…
In this paper we use the parameterization method to provide a complete description of the dynamics of an $n$-dimensional oscillator beyond the classical phase reduction. The parameterization method allows, via efficient algorithms, to…
We study spatial clustering in a discrete, one-dimensional, stochastic, toy model of heavy particles in turbulence and calculate the spectrum of multifractal dimensions $D_q$ as functions of a dimensionless parameter, $\alpha$, that plays…
We provide a protocol to measure out-of-time-order correlation functions. These correlation functions are of theoretical interest for diagnosing the scrambling of quantum information in black holes and strongly interacting quantum systems…
X-ray polarimetric measurements are based on studying the distribution of the directions of scattered photons or photoelectrons and on the search of a sinusoidal modulation with a period of {\pi}. We developed two tools for investigating…
We study geometrical representation of oscillatory integrals with an analytic phase function and a smooth amplitude with compact support. Geometrical properties of the curves defined by the oscillatory integral depend on the type of a…
Orbit separation dimension (OSD), previously introduced as amorphic complexity, is a powerful complexity measure for topological dynamical systems with pure-point spectrum. Here, we develop methods and tools for it that allow a systematic…
The signaling dimension of a given physical system quantifies the minimum dimension of a classical system required to reproduce all input/output correlations of the given system. Thus, unlike other dimension measures - such as the dimension…
I present an extension of the phase distance correlation periodogram to two-dimensional astrometric data. I show that this technique is more suitable than previously proposed approaches to detect eccentric Keplerian orbits, and that it…
We propose a new systematic method of studying correlations between parameters that describe an astronomical (or any) physical system. We recall that behind Dimensionless scaling laws in complex, self-interacting physical objects lies a…
In this letter, we study the case of autonomous agents which are required to move to some new position based solely on the distance measured from predetermined reference points, or anchors. A novel approach, referred to as…
Geometrical model of structure of the universe is examined to obtain analytical expression for the two points nonlinear correlation function. According to the model the objects (galaxies) are concentrated into two types of structure…
Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes like star formation and merging events. Recent studies show…
We calculate correlation functions of exactly-solvable one-dimensional flat-band models by utilizing the "molecular-orbital" representation. The models considered in this paper have a gapped ground state with flat-band being fully occupied,…
In the present article, we investigate the behavior of orbits in a time independent axially symmetric galactic type potential. This dynamical model can be considered to describe the motion in the central parts of a galaxy, for values of…