Related papers: Quantization of Keplerian systems
In previous papers, we developed a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular. We considered systems with well separated components and different initial…
In this paper, we consider a time-periodically forced Kepler problem in any dimensions, with an external force which we only assume to be regular in a neighborhood of the attractive center. We prove that there exist infinitely many periodic…
The goal of this paper is to show how to produce a piece of rigorous bifurcation diagram of periodic orbits for an ODE. We study the Rossler system, one of the textbook examples of ODEs generating nontrivial dynamics, for the parameter…
The paper is continuation of [6] where we have discussed some classical and quantization problems of rigid bodies of infinitesimal size moving in Riemannian spaces. Strictly speaking, we have considered oscillatory dynamical models on…
We give a systematic analysis of forward scattering in 3$+$1-dimensional quantum gravity, at center of mass energies comparable or larger than the Planck energy. We show that quantum gravitational effects in this kinematical regime are…
Combining intervals of ekpyrotic (ultra-slow) contraction with a (non-singular) classical bounce naturally leads to a novel cyclic theory of the universe in which the Hubble parameter, energy density and temperature oscillate periodically,…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
In recent times there has been considerable interest in scenarios for quantum gravity in which particle kinematics is affected nonlinearly by the Planck scale, with encouraging results for the phenomenological prospects, but also some…
Starting with just the assumption of uniformly distributed orbital orientations, we derive expressions for the distributions of the Keplerian orbital elements as functions of arbitrary distributions of eccentricity and semi-major axis. We…
Kepler's orbits with corrections due to Special Relativity are explored using the Lagrangian formalism. A very simple model includes only relativistic kinetic energy by defining a Lagrangian that is consistent with both the relativistic…
A coarsened model for a binary system with limited miscibility of components is proposed; the system is described in terms of structural states in small parts of the material. The material is assumed to have two alternative types of…
The cause for first and second order electromagnetic equivalency of inertial systems is approached from a different point of view than that of special relativity. While special relativity applies dilatation to time and contraction to space…
The energy levels of hydrogen-like atoms are obtained from the phase-space quantization, one of the pillars of the old quantum theory, by three different methods - (i) direct integration, (ii) Sommerfeld's original method, and (iii) complex…
The stellar obliquity of a transiting planetary system can be constrained by combining measurements of the star's rotation period, radius, and projected rotational velocity. Here we present a hierarchical Bayesian technique for recovering…
The first integrals of the Kepler problem are used to compute preliminary orbits starting from two short observed arcs of a celestial body, which may be obtained either by optical or radar observations. We write polynomial equations for…
We investigate the three-dimensional formulation of a recently proposed operational arrival-time model. It is shown that within typical conditions for optical transitions the results of the simple one-dimensional version are generally…
A class of $k$-Essence cosmological models, with a power law kinetic term, is quantised in the mini-superspace. It is shown that for a specific configuration, corresponding to a pressureless fluid, a Schr\"odinger-type equation is obtained…
Classical particle mechanics on curved spaces is related to the flow of ideal fluids, by a dual interpretation of the Hamilton-Jacobi equation. As in second quantization, the procedure relates the description of a system with a finite…
In this contribution, we discuss three situations in which complete integrability of a three dimensional classical system and its quantum version can be achieved under some conditions. The former is a system with axial symmetry. In the…
The possibility of extending the quantum mechanical superposition principle to free parameters such as the cosmological constant appearing in the Lagrangian of physical theories is examined. If the cosmological constant is subject to a…