Related papers: The Kepler problem and non commutativity
Quantum cosmology implies corrections to the classical equations of motion which may lead to significant departures from the classical trajectory, especially at high curvature near the big-bang singularity. Corrections could in principle be…
In this paper, we study how the probability of presence of a particle is distributed between the two parts of a composite fermionic system. We uncover that the difference of probability depends on the energy in a striking way and show the…
Quantum gravitational effects in loop quantum cosmology lead to a resolution of the initial singularity and have the potential to solve the horizon problem and generate a quasi scale-invariant spectrum of density fluctuations. We consider…
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,…
In the present work, we study the noncommutative version of a quantum cosmology model. The model has a Friedmann-Robertson-Walker geometry, the matter content is a radiative perfect fluid and the spatial sections have positive constant…
For a solar-like star, the surface rotation evolves with time, allowing in principle to estimate the age of a star from its surface rotation period. Here we are interested in measuring surface rotation periods of solar-like stars observed…
The non-resonant secular dynamics of compact planetary systems are modeled by a perturbing function which is usually expanded in eccentricity and absolute inclination with respect to the invariant plane. Here, the expressions are given in a…
The orbital evolution and stability of planetary systems with interaction from the belts is studied using the standard phase-plane analysis. In addition to the fixed point which corresponds to the Keplerian orbit, there are other fixed…
Starting from the structural similarity between the quantum theory of gauge systems and that of the Kepler problem, an SU(2) gauge description of the five-dimensional Kepler problem is given. This non-abelian gauge system is used as a…
We review some older and more recent results concerning the energy and particle distribution in ground states of heavy Coulomb systems. The reviewed results are asymptotic in nature: they describe properties of many-particle systems in the…
We consider the Kepler two-body problem in presence of the cosmological constant $\Lambda$. Contrary to the classical case, where finite solutions exist for any angular momentum of the system $L$, in presence of $\Lambda$ finite solutions…
We explore the effects of an undetected outer giant planet on the dynamics, observability, and stability of Systems with Tightly-packed Inner Planets (STIPs). We use direct numerical simulations along with secular theory and synthetic…
We analytically work out the long-term orbital perturbations induced by the first term of the expansion of the perturbing potential arising from the local modification of the Newton's inverse square law due to a topology R^2 x S^1 with a…
We compute the spectrum of cosmological perturbations in a scenario in which inflation is driven by radiation in a non-commutative space-time. In this scenario, the non-commutativity of space and time leads to a modified dispersion relation…
Noncommutativity of the spacetime coordinates has been explored in several contexts, mostly associated to phenomena at the Planck length scale. However, approaching this question through deformation theory and the principle of stability of…
Hundreds of substellar companions to solar-type stars will be discovered with the Kepler satellite. Kepler's extreme photometric precision gives access to low-amplitude stellar variability contributed by a variety of physical processes. We…
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this…
For a Friedman-Robertson-Walker space-time in which the only contribution to the stress-energy tensor comes from the renormalised zero-point energy (i.e. the Casimir energy) of the fundamental fields the evolution of the universe (the scale…
For quantum systems, we expect to see the classical behaviour at the limit of large quantum numbers. Hence, we apply Bohmian approach for describing the evolution of Earth around the Sun. We obtain possible trajectories of the Earth system…
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…